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GEOLOGY
UNIVERSITY OF
ILLINOIS LIBRARY
AT URBANA-CHAMPAIG
GEOLOGY
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Return this book on or before the
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GECLOGY LIBRARY
University of Illinois Library
DEC 30 1964 ‘JUN 4 4/1984
1 7 2004
L161—H41
DIPLOCAULUS
A STUDY IN GROWTH AND VARIATION
EVERETT CLAIRE OLSON
Research Associate, Division of Paleontology
Associate Professor of Vertebrate Paleontology, U niversity of Chicago
FIELDIANA: GEOLOGY
VOLUME 11, NUMBER 2
Published by
CHICAGO NATURAL HISTORY MUSEUM
JANUARY 12, 1951
THE LIBRARY OF THE
FE®& 6 1951
PRINTED IN THE UNITED STATES OF AMERICA
BY CHICAGO NATURAL HISTORY MUSEUM PRESS
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CONTENTS
PAGE
HISTO OFRLLLUSTRATIONS sie coors Re os pete arene ra se ee vs 09
GIST: OF STABLES 52 eh ao ne eee er en Fete a eae ae 59
INTRODUCTIONS: $54 (Gy ors 20 hss ee eke Sen ne oe ea Boek 61
Te YP ROBENMMS ANDO METHODS) oo yee st roe tose eek ese ga a a ee gee 65
General: Problemsi3. 3 ee ee ee eet ee 65
The: Problem:of:Measurements’.. 2 =e oe a et 76
Effect: of:Asymmetry: ofthe Skull-ic. 6 fa Ge a er OS oe 87
Tits REVIEW OF DIPLOCAULUS ere ee ac ere ee eae eles ees 89
Homologies of the: Dermal’ Elements... 2.2.03 see a ie ice hb 89
Review of Named Species of Diplocaulus. . . . ......... 91
TE SPRCIES*AND GENUS foes cen eee tah eee te oe eee tee kal hoe oe 95
SSDOCIOS Sa casa ce ele caer hg pln RW RT aie grea 95
Analynisiote Charactersiacs vat erate gece, eee it tars 96
The Bearing of Ecological Considerations on Group Differentiation. 104
RROUOTNY 6 totes Lore tra bs an Re oh Pp Ma nee, Sole te eS 110
Genus. Fee ee lc ae ee ce Oe be PN ee her eee eae ha 113
Introductionsand Methods? 9: toes cn ey ce et ee 113
Analyaed of Dining) 5 eo ee es es ee ee a es 116
Comparison:of Genera’ 5. (2 se ae ee ne 119
EVie-GROWTHVANDS VARIATION. 930g head ee kn epee, he es ee 133
Method sik Rae tan na oes tta ie sense kare Be See ieee rm, Bonn Re eneniae a Me 133
GrowthiolsS krill ae re Ris ok Rie CAM hs Pare ied ee a ene 136
Analysis Of Growth tik oo cokes aot ee ce ea ne eae 136
Discussion of Changes in Skull Shape ............ 140
The Problem Of Variapiiey pc ss ea ni asune San ene ae ba 144
IRERERENCEShas 225 ey ee ee Cae pee ee 149
57
LIST OF ILLUSTRATIONS
PLATES
1-6. Diplocaulus magnicornis Cope.
7. Diplocaulus brevirostris sp. nov.
TEXT FIGURES
PAGE
Oc, Calter: dinerams ob) este 160 ae Brass ee eed se a 1H
LU Seater diserairia Ol | Gate 4 tore en i ie ea Be he ae ane Ne 78
TiC OCat ler Ginerainis Ol. este S00 12 a5 8s oy ts Sk ee ee ee oo 79
Txes SCAUCOD GINDTRINS OL. PORTO TS AT LO) 8c sg Ue es ng 80
19 -< Sentter cia grarns OL VOnUk 1 OO 2G 6 co in oe he ere, ee. te gr Gees 81
14. meatier dingranis Of. Teste 19'to.20 os, sss) a ee ce 82
15. (Beatter dinorama OF Lents. 10 Gee en ee liv mee ae a eeu s 83
16. Scatter diagram of ratios of Ski/Pmajon Ski . ........2... 99
Lig Scatter diagram: of Sii/Hron Shes 6 3. & bo te Boye Bea esas 101
18. Mean growth stages of Diplocaulus reconstructed from estimating equa-
tions. X14. A, 20 mm. stage; B, 40 mm. stage; C, 60 mm. stage;
D, 80 mm. stage; E, 100 mm. stage; F, 120 mm. stage; G, 140 mm.
BUR GO ie esa he et Sy nop ericson a rede ioe eins eens 138, 139
19. “Stable” and “unstable” parts of growing skulls in Diplocaulus based
onvsOommestage™ crs era sy erin Sits ole i ners hee ie? 140
LIST OF TABLES
1. Constitution of the sample of Diplocaulus .......2.2.2.2..-. 63
2... Measurements: of Diplocaultis..-g0a: 4 6 es ce ee 67-74
3. Crude analyses of twenty-four regressions of Diplocaulus .... . 84-86
4. Natural asymmetry of the interparietal in Diplocaulus ....... 88
B. Ratiog Of:0547/ O-51. 1b: DI OCRMIUR ok. ihe e eh be eos os Sa Bs ote te 96
6. Frequency distribution of Ski/O-Siin Diplocaulus. ......... 96
12s RAUIOS OF SNP UGE DePOCOMINR ea a ae ecw ae a ha Gy ey ae 98
8. Frequency distribution of Ski/Pmziin Diplocaulus ......... 98
9: Ratios OF Ski HEIR: Dinlocgue’ a ee Sg a tS a a 100
L0. Frequency distribution of Ski/Hiin Diplocaulus .......... 100
{1. Linear measurements and ratio Vi/Skiin Diplocaulus ....... . 103
2. Parameters of isogonic regressions of Diplocaulus .......... 116
3. Ratios of skull lengths to four series of measurements in Diplocaulus . 117
59
60
14,
15.
16.
AWE
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
LIST OF ILLUSTRATIONS
. PAGE
Parameters of frequency distributions of ratios in Diplocaulus ... . 117
Measurements of Trimerorhachis ... . he eee ere aren WAL
Values of N and r, for Diplocaulus and Teens Sine Regs + |
Results of tests of significance of differences of ee and eee in Diplocaulus
and Trimerorhachis ... . AZZ,
Results of comparisons of k Cn on " ski) in Desoqulue a Piineie.
TROCIILS!, atten eo ae Seema er BN ida eg eye patel 4A
Results of analysis of variance tent dae. of regression lines of
Tow, Fri, Pai on Ski in Diplocaulus and Trimerorhachis . . .. . . 128
Ratios of skull lengths to four measurements in Trimerorhachis . . . . 126
Parameters of frequency distributions of ratios in Diplocaulus and Tri-
MNETOVROCRIS*8 1a yn Men sae eRe gel Oe a Rae hag a a 126
Results of comparisons of means in Desens and Trimerorhachis . . 126
Comparisons of single specimens of Trimerorhachis with the sample of
TPPLOCHULLS: merits th aan oe Pee ne KoA ee ra tat hg Wat tercre Ok CO
Linear measurements and ratios of Trematops, and significance of
GULeTONGOS: TFOM ROCA MIUR ok oo alae alse di we ee ey 129
Linear measurements and ratios of Batrachiderpeton, and sacs of
Gifferencesifromml pi plocaulus ie. 6 he ote ee . 130
Linear measurements and ratios of Huryodus, and significance of differ-
CHEER TOI LE TIOCUNE URES porn ee oe! hs seo ee pap ee Oe ie shone oe 131
Measurements of skull width (W) in Diplocaulus .......... 135
Measurements of skull length (LZ) in Diplocaulus ......... . 185
Values for plotting mean skull stages of Diplocaulus ....... . 188
INTRODUCTION
Recent years have seen a marked increase in efforts to treat
paleontological materials quantitatively. Impetus to this trend was
provided by the publication of Quantitative Zoology, by Simpson and
Roe (1939). Although many paleontologists have been slow to
follow the trend, it has become clear that a quantitative approach,
if properly handled, can yield results of great significance in at
least some phases of both invertebrate and vertebrate paleontology.
I have been inclined to the opinion that such studies could have but
limited application in my field of principal interest, the study of
late Paleozoic tetrapods, since samples are commonly small, distor-
tion extensive, and preservation poor in many instances. The
present study was undertaken primarily to test the utility of quantita-
tive work in analyses of a sample of early tetrapods.
Diplocaulus, a rather highly specialized early Permian amphibian,
was selected for this study for several reasons. It is one of the most
common genera in the Early Permian beds of Clear Fork age, and
both large and small skulls have been obtained. This has made
possible a study of growth within the species of the genus. Secondly,
members of the genus have been reputed to exhibit high variability,
a feature that seems to be expressed, perhaps less strikingly, in a
number of Permian genera, such as Captorhinus and Diadectes. The
taxonomy of the genus Diplocaulus appears to be in an unsatis-
factory state as a result of this supposed variability, and an oppor-
tunity to test quantitative methods in the solution of taxonomic
problems as well as in the interrelated problems of growth seemed
to be at hand. Diplocaulus has certain disadvantages. Very little
has been known of the genus from other horizons, so that comparison
of samples from different stratigraphic levels is not practical. Re-
cently, a collection of several skulls has been obtained from the
Vale, which overlies the Arroyo, the source of the sample studied.
These skulls will form a basis for comparison once they have been
orepared, but they are not considered in the present paper. The
1abits of Diplocaulus are poorly understood, and the functions of
‘ertain parts of the skull have not been explained adequately.
61
62 FIELDIANA: GEOLOGY, VOLUME 11
More complete interpretation is desirable for analyses of the relation-
ships of function and variation. Nevertheless, Diplocaulus is one
of the best Permian genera now available for quantitative studies.
MATERIALS
Forty-seven skulls and partial skulls compose the sample treated
in this report. Pertinent data concerning numbers, localities, and
ownership are presented in Table 1. The skulls are figured in plates
1 to 7. Normally, such a complete pictorial record would not be
required, but the complete series has been figured in order that the
reader may fully understand the state of preservation of materials—
an item of considerable importance in evaluating results. In the
drawings, particular attention has been paid to accuracy of outline
and osseous patterns. The pitted surface pattern has been omitted
from the figures since it adds to the difficulty of interpretation of
the dermal patterns.
All specimens of the sample have come from the Arroyo Forma-
tion of the Clear Fork. Precise data on localities are not available
for many of the specimens, although it is possible to locate all but
a few to within about one-half mile of the place in which they were
collected. There is likewise little direct evidence concerning the
nature of occurrence. This may, however, be reconstructed in part
from the matrix, which has not been completely removed in most
instances. In the present study it has been assumed that the speci-
mens of the sample have been drawn from a fauna with lateral and
limited vertical continuity. The lateral distribution over the
restricted area from which the collections were made appears to have
been continuous, and vertical continuity is suggested by the limited
section from which the specimens have been drawn and by the fact
that there are few evidences of change in other groups within the
confines of the Arroyo beds. Analyses of Diplocaulus give no evidence
of differentiation on the basis of localities.
The amount of preparation of different specimens varies widely.
Those prepared solely for the present study, about half of the sample,
have only their dorsal and lateral surfaces cleared of matrix. A few
of the others are fully prepared. Extensive plaster reconstruction
has been done on some specimens that were mounted for exhibition,
and certain restorations are clearly faulty. Distortion is evident in
a number of specimens. Specimens in which either reconstruction
or distortion was excessive were eliminated from the sample. In
addition to those that form the sample, about fifty specimens were
LORI Sl WE peg alt Rt. bie
OLSON: DIPLOCAULUS 63
TABLE 1.—CONSTITUTION OF THE SAMPLE OF DIPLOCAULUS
Specimen Specimen
number Locality number Locality
C.N.H.M.-U.C.! A.M.
2062 oe ee: Craddock: Ranch? +4466) 3-00) 2, oer ee ?Coffee Creek
9A NESS re fae ele Gua ale Craddock: Ranch: “4467.4 48 4. ae Coffee Creek
Dee eee Recr foo ke Craddock Ranch 4469............... East Coffee Creek
PAREN ER Ber aM ew eel Craddock: Ranch 4470.22 272" 4 ae East Coffee Creek
ZL ee ae er ee Coffee Creek? 4472......................Hog Creek
ALORA teres Craddock Ranch 4418535. a eee Uncertain
B64 a leona Shee: CraddockiRanch. “448400 ern toe see Coffee Creek
GEG pat ce ne enhcoeee tes Collide Creek: 24486 0 cn cet Aes Hog Creek
Sala ee en Data Coffee Creek:. “4402. os ee East Coffee Creek
LOUD. res ee Re ees Beaver Creek 4494................... 2Coffee Creek
ee Peet eee eee ees igre ar 498 5 ena s vay oes Oreek
A natn etal ae 32 pretreat a oe ony Cree
UGAS oe eek Craddock Ranch BOOP iancciha niet te oye e ees
: 4504...............West Coffee Creek
1650 ee ea ee Middle Coffee Creek
BO cr eer Ce oe Clear Fork?
166200 oer West Banks Brushy Creek 4512 Clear Work
115% Rear ie a ose et Coffee Creek Retina cee ea meee
GOODS wee So iene hast; Cofiee: Creel: ee ae eres Ei neaananeahh é
1656.... Ge pa eR _Middle Coffee Creek 4523A Siena, FoR Sua ee he evens Baylor County
TOR G ts NS ede Ue Coffee Creek 4528B.................Baylor County
(6560-0 ee oe Clofiae Cronies 2000 coins as dooneee pale: Uncertain®
1660.55) 2+ Miliddle: Coffea Crock: 408 Tassie crrenee cei ee: Grey Creek
1 GGUS ee Middle Coffee Creek 4589......................Clear Fork
L668 5. es Be et Middle:Coffes' Creek: -4597; = ..3 nes en eClear Nork
PLZ689 ere era Coffee:Creek: "4752.0. 2 sce ee Uncertain
1C.N.H.M.-U.C.: The collection thus designated was recently presented to
Chicago Natural History Museum. The numbers, with U.C. as collection designa-
tion, are not to be changed. P=paleontological collections at Chicago Natural
History Museum. A.M.=American Museum of Natural History.
2 The locality markings on a number of specimens do not give an adequate
idea of their precise position. The general designation of Coffee Creek places
the locality north of the Wichita River in the area drained by Coffee Creek. In
some instances it refers to the principal valley that lay just north of the river
prior to the development of Lake Kemp. In others, it refers to a locality that lay
north of this on one of the three main branches of Coffee Creek, respectively
noted as East, Middle and West Coffee Creek in other designations. All speci-
mens so labeled come from approximately the same horizon over an area about
five miles on a side.
5 Several specimens are merely labeled Clear Fork. Since there was no collect-
ing in the Vale or Choza during the time that they were gathered, this designation
refers either to the Clyde or the Arroyo. It is clear from the matrix of the speci-
mens so listed that they are from the Arroyo and most of them appear to have
come from south of the Wichita River, from the broad area occupied by the breaks
of Brushy Creek.
4 This listing si almost no information of stratigraphic value. The two
specimens so listed appear to have come from north of Seymour. On the basis
of the matrix the most probable locality is the Craddock Ranch.
* This specimen is listed as from the Wichita Basin. The matrix places it
ilmost certainly in the Arroyo. No. 4752, also listed as uncertain, merely has
he label “‘Texas.”” It also is quite surely from the Arroyo, but its locality is most
incertain.
64 FIELDIANA: GEOLOGY, VOLUME 11
available, but all were eliminated from consideration for these reasons
or because of incompleteness, which made certain key measurements
impossible.
ACKNOWLEDGMENTS
Many of my colleagues have given much time and effort to aid
in the preparation of this paper and several institutions have made
their collections available for study. Dr. Rainer Zangerl of Chicago
Natural History Museum has been a consultant and with Mr.
Robert F. Inger has taken X-ray photographs of the sample of
Bufo marinus from the collections of the Museum. Dr. Edwin H.
Colbert of the American Museum of Natural History, Dr. Claude W.
Hibbard of the University of Michigan and Dr. Alfred S. Romer of
Harvard University have supplied measurements of the amphibian
Trimerorhachis for comparative purposes. I am deeply indebted to
Mr. Robert Miller of the University of Chicago for his aid in many
phases of the work. Dr. Sewall Wright and Dr. W. Allen Wallis,
also of the University of Chicago, have been helpful in suggesting
procedures in the statistical work.
Both Mr. Robert Miller and Mrs. Phyllis Hull have rendered
valuable assistance to me in doing the calculation. The drawings for
the illustrations were made by Mr. Melvin Douglas of Chicago, except
figures 18 and 19, which are the work of Mr. John Conrad Hansen,
Staff Artist, Chicago Natural History Museum.
Specimens were made available by the American Museum of
Natural History, the University of Michigan, Harvard University
and the United States National Museum. The remainder of the
sample was drawn from collections recently transferred to Chicago
Natural History Museum from the University of Chicago.
To each of the individuals who has participated in the work and
to the institutions that graciously supplied specimens, I express my
deep and sincere appreciation for their co-operation in helping me
to bring this project to completion.
I. PROBLEMS AND METHODS
GENERAL PROBLEMS
It is well understood that the amount of variability in different
genera and species differs widely—that some groups are notably
stable and others highly varied. The scope of variability and tests
of homogeneity and heterogeneity of populations can best be ex-
pressed by standard statistical parameters based upon analyses of
samples drawn from natural populations. It has appeared to many
students of Permian vertebrates that extensive variation at the
species level is a common phenomenon in animals from that Late
Paleozoic period, but how much of the variation is real and how much
is merely apparent has not been demonstrated. I, among others,
have adopted a conservative policy of referring closely similar
variates, within reasonable limits, to a single species, on the assump-
tion that real differences, if present, cannot be demonstrated.
Recent work on Diadectes (Olson, 1947) is a case in point. Dziplo-
caulus appears to provide a sample adequate for checking this taxo-
nomic procedure, and there is reason to suppose that the methods
developed and the conclusions reached during the work will aid in
the study of less adequately known genera.
The several interrelated problems involved in this analysis con-
sist of the determination of the taxonomic relationships of the speci-
mens involved, the determination of differences that have been
variously interpreted as specific and individual, the analysis of the
development of these differences, and investigation of the reasons
for their existence. Inasmuch as this study was undertaken as a
test case and much of the work proceeded by trial and error, the
methods and results are recorded somewhat in the form of a case
history of the investigation. Preliminary steps are outlined in the
present section. The second section consists of a summary of
pertinent earlier studies on Diplocaulus, with comments on homol-
ogies of cranial elements and on taxonomy. The third section in-
cludes an analysis of the taxonomy, based in part on numerical data,
with discussions of the characteristics of the genus and its species.
Although such an analysis was not the primary objective of the
65
66 FIELDIANA: GEOLOGY, VOLUME 11
investigation, it is obviously impossible to study the growth of a
species without an understanding of taxonomy. The fourth section
comprises a study of growth of the skulls of one species of Diplocaulus
and the bearing of the changes upon the supposed high variability
of the species. Separation of the third and fourth sections is some-
what artificial, for taxonomy cannot be studied in most fossil am-
phibians and reptiles without taking growth into consideration. It
has become increasingly evident, as the study has developed, that
analyses of growth are of prime importance in studies of extinct
amphibians and reptiles. There are, of course, no osseous structures
that do not change as growth proceeds, no convenient organs, such
as the enamel-covered teeth of mammals, which are unchanged
except by wear after eruption. There is, furthermore, no definable
terminal growth in members of these classes and no characters
specifically definitive of skeletal maturity. Analyses which do not
take growth factors into consideration will, in many instances,
reach faulty conclusions.
Growth in fossils is, however, extremely difficult to study.
Obviously, no time scale is available. It is, perhaps, possible to
obtain some measure of relative time series, but the methods present
serious difficulties in materials such as those considered in the present
paper. Thus it is necessary to use the changes of one or more
structures as a substitute scale. Characters selected in this capacity
assume the role of independent variables, although there may be
little justification for their selection in this capacity. A further
problem in growth studies arises from the difficulty of adequate
sampling—sampling that will include a wide series of growth stages.
One gains the impression that the great majority of fossil amphibians
and reptiles fall near the upper limits of growth for their particular
species. While this is less true than descriptions would suggest, it
does appear that most specimens fall within the upper 30 per cent
of the probable size range of their group based on such linear features
as over-all length, skull length, ete. Much may be done even within
such limits but, as will be shown below, many significant features
have their origins well below such a limit. This problem was not
critical in the case of Diplocaulus, since the available specimens
range from 14 to 147 mm. in skull length, with fair distribution
throughout the size range. This unusual distribution makes the
genus especially advantageous for study.
With these more general considerations in mind we may turn to
problems more specifically concerned with the study of Diplocaulus.
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OLSON: DIPLOCAULUS 73
EXPLANATION OF SYMBOLS AND MEASUREMENTS
Explanation of symbols.—Subscripts: 1=length; w=width; p=posterior; a=
area; x=axis. Others: *=measurement approximate; L=left; R=right; for Ski
Skw, Pi-Fr, etc. see descriptions of measurements below.
Procedures in measurement.—All measurements are in millimeters and areal
measurements in square millimeters. Linear measurements have been made with
sliding calipers, angular measurements with a standard protractor, and areal
measurements with a planimeter. Measurements represent the mean of a minimum
of three trials. All measurements were made on a plane tangent to the dorsal
platform of the skull, as if the skull were projected onto this plane by orthogonic
projection.
Ski=Skull length. The distance from the tip of the snout at the intersection of
the suture between the premaxillaries to the posterior margin at the inter-
section of the suture between the interparietals.
Skw=Skull width. The distance between the horn tips.
Pi-Fr=Pineal-frontal length. The distance from the anterior margin of the pineal
opening to the frontal-parietal suture at the junction of the suture between
the parietals.
Ipi=Interparietal length. The distance from the anterior termination of the
suture between the interparietals, at the point of intersection of the more
posterior interparietal-parietal suture, and the posterior termination of the
suture between the interparietals.
Pai=Parietal length. The distance from the intersection of the suture between
the parietals and the parietal-frontal suture and the junction of the suture
between the parietals and the more anterior parietal-interparietal suture.
Fri= Frontal length. The length of the frontal bone along the midline of the skull.
O-Si=Orbito-snout length. The distance along the midline of the skull from a
plane tangent to the anterior margins of the two orbits to the tip of the snout.
Iow=Interorbital width. The minimum distance between the inner margins of the
orbits normal to the axial plane of the skull.
~ Ow=Orbital width. The greatest width of the orbit along a line normal to the
| axial plane of the skull.
O1=Orbital length. The greatest length of the orbit along a line parallel to the
axial plane of the skull.
Pmxi=Premazillary length. The distance between the posterior termination of
the suture between the premaxillaries and the intersection of this suture
with the tip of the snout.
Varw=Narial width. The least distance between the inner margins of the nares.
-ofa=Postfrontal area. The area of the postfrontal to the nearest square milli-
meter as measured by planimeter.
74 FIELDIANA: GEOLOGY, VOLUME 11
Poi=Postorbital length. The distance from the midpoint of the postfrontal-
postorbital suture to the termination of the posterior spur of the postorbital.
Poa=Postorbital area. Measured as in the case of the postfrontal.
Paw=Parietal width. The distance from the suture between the parietals normal
to the midline of the skull to the point of junction of the parietal, the squa-
mosal, and the supratemporal.
Paa=Parietal area. Measured as in the case of the postfrontal.
Ipw=Interparietal width. The distance from the level, on the midline of the skull,
of the posterior termination of the suture between the interparietals normal
to the midline of the skull to the greatest lateral extremity of the interparietal.
Sti=Supratemporal length. Distance from the junction of the parietal, the inter-
parietal and the supratemporal to the tip of the horn.
Z1=Parietal angle. The acute angle between the midline of the skull and a line
from the tip of the snout, at the midline, to the junction of the parietal,
the supratemporal and the squamosal.
22=Interparietal angle. The acute angle between the midline of the skull and
a line from the tip of the snout, at midline, to the lateral extremity of the
interparietal.
Z3=Postorbital angle. The acute angle between the midline of the skull and a
line from the tip of the snout, at midline, to the posterior termination of the
postorbital.
Z4=Supratemporal angle. The acute angle between the midline of the skull and
a line from the tip of the snout, at midline, to the horn tip.
Z5=Interparietal posterior angle. The acute angle between the midline of the
skull and a line between the posterior termination of the suture between the
interparietals and the lateral extremity of the interparietal.
Z6=Supratemporal posterior angle. The acute angle between the midline of the
skull at the level of the posterior termination of the suture between the
interparietals and the horn tip.
Z7=Postorbital axial angle. The acute angle between the midline of the skull
and a line through the midpoint of the postfrontal-post orbital suture and the
posterior termination of the postorbital as marked by the postorbital spur.
Z8=Interparietal axial angle. The acute angle between the midline of the skull
and a line through the midpoint of the suture between the interparietals and
the lateral extremity of the interparietal.
Z9=Parietal axial angle. The acute angle between the midline of the skull and
a line through the center of the pineal opening and the point of junction of
the parietal, the squamosal and the supratemporal.
OLSON: DIPLOCAULUS 75
Members of this genus show undeniably striking differences in various
characters, even when specimens of approximately the same size are
compared. A cursory study seemed to indicate the alternatives in |
taxonomic procedure of recognizing a large number of species, ten
or more, or of lumping all specimens into a single species. The
presence of a large number of species of a single genus in a limited
area and from beds of restricted vertical extent seemed improbable,
so that the second alternative was adopted as a working hypothesis.
Early studies tended to support the hypothesis but later work
proved it, as well as its alternative, to be false. The specimens
appear to represent two species, one including the majority of the
specimens and the other a very few.
Initial problems in any study involving numerical data derived
from measurements concern the unit or units of measurement and
what to measure. Linear measurements throughout the paper are
expressed in millimeters, a unit suitable to the range of sizes en-
countered. The problem of what to measure is particularly acute
in animals such as Diplocaulus, in which there is little or no directive
evidence to show what measurements and what comparisons might
prove valid and useful. No real progress could be made until this
problem had been settled, and considerable time was spent in random
testing before it was solved. Certain possibilities were at once ap-
parent: midline characters appeared to be stable; the length of the
pre-orbital region, the skull width, the posterior curvature and
certain others showed possibilities of discontinuous differences. A
number of these were tested without definitive results, strengthening
the working hypothesis that there was a single species. Eventually
the early efforts of rigid analysis were temporarily abandoned and a
series of twenty-seven measurements was made on each skull, in
so far as this was possible. Since no skull showed all twenty-seven
features, the size of the sample was somewhat reduced for any one
series of measurements. The twenty-seven measurements were
selected primarily on the basis of ease and accuracy of measurement.
Linear, areal and angular measurements were used. Skull length,
measured along the midline, was taken as the base measurement
for comparison and was, in most cases, used as the independent
variable. Measurements were then co-ordinated in a series of twenty-
four tests that consisted in each case of the regression of the measure-
ment in question on skull length. Each test was plotted as a scatter
diagram on arithmetic, metric graph paper to give a basis for visual
evaluation of the nature of the regression and the general correlation
of changes in each series of measurements with changes in skull
76 FIELDIANA: GEOLOGY, VOLUME 11
length (see figs. 9-15). In some instances coefficients of correlation
(r) were determined, as well as such items as regression coefficients
(byx and byy) and standard deviation (c), but for the most part
these were not necessary in preliminary analysis. | Curves were
fitted to the scatter diagrams by the crudest methods. From the
scatter diagrams a table of twenty-four tests was prepared by en-
tering an estimate of the deviation of each specimen from the roughly
plotted curves. O was used to indicate little deviation and the
letters S, M, and L to indicate small, medium, and large deviations
respectively. A plus (+) or minus (—) sign was used to indicate
whether the deviation fell above or below the line of regression
respectively. Each test was then studied in terms of its deviations
in individual tests. From this work it became apparent that certain
specimens might be different from the majority but that only a
few of the twenty-four tests could be of value in a possible separation
of the sample into two or more groups. Four tests were selected as
possessing potentialities for this use. Each was then analyzed
carefully and two of the four were discarded as indecisive. The
remaining two suggested other tests; new measurements were made
and new tests conducted. The crude analyses and their results are
shown in Table 2; the measurements that were used are shown in
Table 3.
At this point in the study the outlines of the taxonomy were
apparent and the groundwork had been laid for quantitative studies
of growth within a single species. The detailed work involved in
the preliminary studies and in development of the suggestions ob-
tained from these studies is given in the section on taxonomy and
needs no further consideration at this point.
THE PROBLEM OF MEASUREMENTS
Only the dorsal dermal surface of the skull has been used in this
study, for several reasons. Differences in skull shape, in position
of the fossae of the sense organs, and in dermal patterns are all
apparent in this aspect. The dorsal surface is usually well preserved
and sutures are present in most skulls. In contrast, the occipital
and palatal surfaces are poorly preserved in most specimens and, in
many instances, do not permit easy differentiation of the component
elements. Certainly, many more characteristics could be studied,
but mere number becomes unimportant in view of the variety avail-
able on the dorsal surface and the fact that certain of these are of
critical importance.
——
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Fic. 10. Scatter diagrams of Tests 4 to 7.
78
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Fic. 11. Scatter diagrams of Tests 8 to 12.
79
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81
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82
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85
86 FIELDIANA: GEOLOGY, VOLUME 11
Even when measurements are restricted to the dorsal surface of
the skull a number of problems remain. Distortion is recorded, of
course, in any direct measurement. No attempt has been made to
eliminate this effect, since any such effort would result in a subjective
bias. Thus, the effects of distortion appear in the tabulations and
calculations. For the most part the effects in the sample are rela-
tively unimportant. More difficult problems are posed by the lack
TESTS
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TABLE 3b.—CRUDE ANALYSES OF TWENTY-FOUR REGRESSIONS OF DIPLOCAULUS
of complete specimens. The midline length is extremely important,
since it is one of the two variables in most of the regressions, but it
cannot be obtained, because of breakage, for many skulls in collec-
tions and for this reason a number of specimens that would other-
wise have proved of some value have not been included in the
sample. In some instances it has been possible to make a close
estimate of this value. These estimates have been checked in so
far as possible by introduction of the specimens in regressions
calculated without use of the estimated value. Estimates of other
values, particularly skull width, have been used where they have
been considered essential. All estimated values are specified in the
table of measurements, Table 2.
Measurements of dimensions of individual bones pose several
problems, since there are differences not only in size, but in propor-
tion and shape as well. The technique has been to use a point or
points that can be identified on homologous bones in all specimens
in which the character is shown; for example, in the case of the
anterior margin of the postorbital, a point midway between the
OLSON: DIPLOCAULUS 87
junction of the limiting suture with the postfrontal has been selected.
For the postero-lateral termination of the parietal, the junction of
the sutures separating the parietal, squamosal and supratemporal
(tabular) was used. The most difficult measurements are those con-
cerned with the outline of the skull. Special techniques, as discussed
on page 133, were used. The problem of measurement is com-
plicated by the fact that the dermal bones of the skull make contact
with pronounced overlap, and any wear of the skull, prior to col-
lecting or in preparation, tends to shift the position of sutures from
that occupied when the surface was intact. No attempt to estimate
the amount of shift has been made, so that any errors introduced
by the factor of wear enter into the recorded measurements.
In spite of all these difficulties of measurement, typical of many
paleontological samples, the results obtained appear to have validity.
They provide an answer to the question that was uppermost in my
mind at the time the work was undertaken, the question as to
whether or not the nature of the materials would be such that
significant results could be obtained.
EFFECT OF ASYMMETRY OF THE SKULL
Bilateral asymmetry must be taken into consideration in the
measurements. Such asymmetry appears in the skulls of Dzplo-
caulus as the result of three major effects: (1) the natural asymmetry
apparent in the sutural patterns; (2) injuries during growth; (3)
differential distortion after death. In making measurements the
effects of asymmetry have been handled in various ways. If one
side of the skull has been badly distorted while the other has suffered
less, measurements have been based on the well-preserved side only.
This obviously introduces a subjective analysis of the nature of
distortion, but this is preferable to the drastic effects of entering
measurements profoundly affected by damage. In cases in which
there has been some distortion of both sides, but the distortion |
appears to have been somewhat compensatory, total raw measure-
ments have been used without modification. In instances in which
homologous elements on the two sides of such a skull were measured,
mean values have been used. Skulls evidently highly distorted in
any particular measurement have not been used for that measure-
ment, but only extreme cases have been eliminated. In cases in
which injuries have introduced an abnormality on one side, measure-
ments have been based on the side not affected.
88 FIELDIANA: GEOLOGY, VOLUME 11
The case of normal asymmetry introduces other problems. These
are well shown in the pattern of the midline sutures; for example,
the anterior end of the suture between interparietals lies to the right
of the midline in some specimens and to the left of the line in others.
I have referred to individuals with the interparietal suture to the
left as sinistral and to those with the suture to the right as dextral.
It is possible to divide the skulls of Dzplocaulus into three groups
on this basis (see Table 4). It appears unlikely that asymmetry
has resulted from any profound genetic difference, since the grouping
that it suggests does not correspond with the one inferred from
studies of several other features of the skull. |
TABLE 4.—NATURAL ASYMMETRY OF THE INTERPARIETAL IN DIPLOCAULUS
Approaching Not
symmetry Dextral Sinistral determinable
A.M. 4589 P12689 U.C. 410 UWCS222
UC .221 U.C. 229 A.M. 4467 U.C. 637
A.M. 4491 A.M. 4472 A.M. 4523A A.M. 4494
U.C. 1663. A.M. 4523B A.M. 4589
A.M. 4512 A.M. 4501 U.C. 10138
U.C. 1650 U.C. 1648 A.M. 4484
A.M. 4470 U.C. 564 A.M. 4485
U.C. 1661 U.C. 1015 U.C. 1654
A.M. 4752 U.C. 1655 U.C. 1660
U.C. 206 U.C. 6386 U.C. 1652
A.M. 4473 U.C. 1658 U.C. 1317
A.M. 4514 U.C. 223 A.M. 4530
A.M. 4511
U.C. 1656
A.M. 4504
A.M. 4469
A.M. 4498
A.M. 4466
Linear and angular measurements are, however, affected by this
asymmetry and in most instances differ somewhat on the two sides
of a single individual. It is possible, of course, to base all studies
of the skulls on measurements of comparable sides, but it has been
‘ found that little is gained by such a procedure and that the results
do not have a value that compensates for the new problems intro-
duced. My practice has been to use the mean of the two values in
all cases in which measurements of the same feature on two sides
of the skull show differences.
II. REVIEW OF DIPLOCAULUS
HOMOLOGIES OF THE DERMAL ELEMENTS
Much has been written on the homologies of the skull elements
of Diplocaulus and few of the bones of the dorsal dermal surface
pose any problems. The figures of Williston (1909) and Douthitt
(1917), based principally on U.C. 636, show elements in typical
relationships, although they do not, of course, show variations in
proportionate size and shape. The principal differences in the figures
of various writers, so far as the limits of bones are concerned, occur
in the analyses of the snout. Case (1911) shows a suture limiting
the anterior margins of the median elements lying immediately
anterior to the frontal, while Douthitt does not show this suture.
As a consequence of the difference in interpretation, Case designates
this pair of bones as nasals, while Douthitt, following Williston,
recognizes but a single pair of bones—premaxillaries—that include
the nasals and premaxillaries of Case. A study of the skulls now
available, a series much more extensive than any available to Case,
Williston, or Douthitt, confirms the determination that no suture is
present and that the nasals are missing.
Another point of controversy concerns the two bones that lie
posteriorly and postero-laterally to the orbits on each side of the
skull. The bone that lies just behind the orbit gives the appearance
of being a postorbital; if so, the element behind it would then have
to be called supratemporal (see Romer, 1933, for example). The
alternative explanation advanced by Watson (1913) and adopted by
Douthitt (1917) appears to be more sound. The element behind
the orbit appears to be the postfrontal and the bone postero-lateral
to it the postorbital, which has been excluded from the circum-
orbital series. The relationships of the two elements to each other
and to surrounding bones suggest these identities. The postfrontal,
according to this interpretation, is in contact with the frontal
medially, the parietal postero-laterally and posteriorly, the jugal
laterally and the bone identified as postorbital postero-laterally.
The postorbital of this interpretation is in contact with the parietal
medially, the squamosal postero-laterally, the jugal antero-laterally,
89
90 FIELDIANA: GEOLOGY, VOLUME 11
and the postfrontal antero-medially. All of these relationships are
normal for these two bones in the amphibians, except for the jugal
contact of the postfrontal and the parietal contact of the postorbital.
Loss of the supratemporal has resulted in the latter contact in various
genera. Interpretation of the more posterior element as supra-
temporal implies changes in which the contact with a tabular and
an interparietal was lost. While this is possible—by elongation of
the parietals, interparietals and tabulars—the conditions in related
genera suggest that it is not what occurred. The most probable
explanation is that given by Watson on the basis of Batrachiderpeton.
This genus lacks the supratemporal (as identified by Watson) but
has undoubted postfrontals and postorbitals. The orbits are lateral.
As Watson has pointed out, migration of the orbits to a dorsal posi-
tion separating the prefrontals and postfrontals and isolating the
postorbital from the orbital margin would produce a condition like
that of Diplocaulus. On these bases it appears that the element
variously identified as supratemporal and postorbital is in reality
postorbital. This terminology is followed in the present paper.
If the identity of the so-called supratemporal is in error, there
remains in the temporal region of Diplocaulus but one element of
' the intertemporal, supratemporal, and tabular series characteristic
of many amphibians. In this respect the genus agrees with the
gymnarthrids... The bone that forms the “horn” has commonly
been called tabular, but in the gymnarthrids it is tentatively identi-
fied as supratemporal. If the second of the small elements behind
the orbit were supratemporal there would be no choice but to call
the more posterior bone tabular, but this does not appear to be the
case. It is not unreasonable to assume that this single element of
the temporal series is actually homologous in the various groups of
lepospondyls. There is, however, little real basis for determination
of the homologies of the bone. If it be assumed that the gymnarthrids
and diplocaulids arose from a group in which intertemporal, supra-
temporal, and tabular were present, as is suggested by the almost
certain origin of the tetrapods from rhipidistians, it must follow that
two of the three bones were lost. Since there is no bone with the
1JIn a recent paper, Gregory (1948) has referred the Microsauria, including
the Gymnarthridae, to the class Reptilia. His evidence strongly supports the
assignment so far as at least some of the groups called microsaurs are concerned.
The gymnarthrids, however, have certain features of the occiput, palate and
dermal skull surface that suggest amphibian affinities. It may be that the gym-
narthrids and the other families, usually considered as microsaurs, are not closely
related. Detailed investigation of the skulls and vertebrae of the gymnarthrids
must be made before this matter can be resolved.
OLSON: DIPLOCAULUS 91
relationships of the intertemporal, we may safely assume that this
was one of the two. The tabular persistently makes contact with
the interparietal medially, the supratemporal anteriorly, and the
squamosal laterally in forms in which both supratemporal and
tabular are present. The supratemporal lies between the inter-
parietal and squamosal and meets the intertemporal anteriorly. If
either the tabular or supratemporal were lost, and the other in part
occupied its position, the condition in the gymnarthrids and Diplo-
caulus would obtain. In amphibians in which two of the three
elements are present, the tabular tends to be restricted to the postero-
lateral corner of the dorsal platform. Rarely does it make contact
with the parietal in spite of the progressive restriction of the posterior
part of the skull. The supratemporal, on the other hand, maintains
contact with the parietal and squamosal. It is this general tendency
that had led to the tentative identification of the single bone in the
gymnarthrids as supratemporal. The difference between the condi-
tions of the gymnarthrids and Diplocaulus is primarily that, in the
latter, the element is isolated from the postorbital and postfrontal.
This could have resulted from the extensive lateral growth of the
parietal. The case for calling the element in question supratemporal
is as strong as that for calling it tabular. In view of the probable
identification of the comparable bones in the gymnarthrids as supra-
temporals and of the evidence of relationships between the gym-
narthrids and diplocaulids, the balance seems to favor homology
with the supratemporal. This identification is used throughout the
present paper.
REVIEW OF NAMED SPECIES OF DIPLOCAULUS
The genus Diplocaulus was proposed by Cope (1877) for D. sala-
mandroides, a species based on a few vertebrae and part of a lower
jaw from the Late Pennsylvanian beds of Vermilion County, Illinois.
Subsequently, he described two species from the Permian of Texas,
D. magnicornis Cope (1882) and D. limbatus Cope (1896). Broili
(1904) added two more species from Texas, D. copei and D. pusillus.
Case (1911) summarized and revised the work on the genus up to
1911; he pointed out that D. copei was indeterminate, since the
three specimens described could not be distinguished from D. magni-
cornis and D. limbatus, and suggested that D. pusillus was of very
uncertain assignment and might even be referable to the Family
Trimerorhachidae. He recognized both of Cope’s Permian species,
contrasting them as follows:
92 FIELDIANA: GEOLOGY, VOLUME 11
D. limbatus Cope
1. Horns terminating in a point and curved inward at ends. The posterior
edge of the skull more sharply concave.
2. Anterior edge of the frontal bone but little anterior to the orbit.
3. Vomerine teeth arranged in segment of a broad curve.
4. Anterior end of skull a segment of a broad curve.
5
6
: or eas of the facial region distinctly radial from a point between the
orbits.
. Orbits larger.
D. magnicornis Cope
1. Horns terminating more bluntly or with spatulate ends. Not curved
at ends. The posterior edge of the skull with a wide concavity.
. Anterior edge of the frontal nearly midway between the orbits and the
nares.
2
3. Vomerine teeth arranged as wide V with apex forward.
4. Anterior edge of skull sharper.
5. Sculpture of facial region not distinctly radial.
6. Orbits smaller.
Most of these supposed differences appear to be valid when viewed
on skulls as distinctly different as those that Case was studying.
Additional specimens have shown that there is actually a much
greater degree of intergradation in most of the characters.
The most recent comprehensive review of the genus Diplocaulus
was published by Douthitt (1917). He stated that the only valid
character cited in Case’s differentiation of D. limbatus and D. magni-
cornis is the nature of the postero-lateral horns of the skulls and that
even this character will not invariably serve to differentiate skulls.
He concluded, however, that there was no reason to question the
distinctness of the two species. Douthitt accepted D. pusillus as
distinct but agreed with Case in questioning the generic reference.
Relatively little taxonomic work on Diplocaulus has been done
since the publication of Douthitt’s paper. In 1918 Williston de-
scribed two small skulls, U.C. 206 and 207, and assigned them to a
new genus and species, Platyops parvus Williston. Case (1946)
called attention to the fact that Platyops was preoccupied and pro-
posed the generic name Permoplatyops to replace Platyops Williston.
As will be shown, Permoplatyops seems to be an immature representa-
tive of the genus Diplocaulus and specifically the same as many of
the larger skulls.
Mehl (1921) described a new species, D. primigenius Mehl,
naming U.C. 564 as the type. The characters of the neural spines
and the size and proportions of the vertebrae were considered defini-
tive. The skull of this specimen is used in the present study and is
OLSON: DIPLOCAULUS 93
shown to be a normal member of the more common species. The
vertebrae, it is true, pose some interesting problems. Their bearing
on taxonomy is discussed below (p. 102). There is no basis for separa-
tion of Mehl’s species from D. magnicornis on the basis of the skull,
and analysis of the vertebrae will show that the supposedly definitive
characters are subject to another interpretation.
The type of D. limbatus Cope, A.M. 4471, consists of a rather
poorly preserved skull and lower jaws with vertebrae and part of
the shoulder girdle. Few measurements could be taken on the speci-
men; only the length, orbito-snout length, approximate width of
the skull at the termination of the horns, and interorbital width are
sufficiently well shown to provide a basis for measurement. Much
of Case’s revised description was based on referred specimens A.M.
4470 and 4542.
The type of D. magnicornis Cope is listed by Case as A.M. 4472.
This is an excellent skull (see pl. 5). The specimen labeled as
the type in the American Museum of Natural History, however, is
A.M. 4539. The species was described in 1882 and A.M. 4472 was
not collected until 1896. This has been confirmed by examination
of the field notes of C. Sternberg, the collector. The type consists
of skull parts, vertebrae and other fragments. Efforts have been
made to reconstruct the skull, which is large, perhaps 115 to 120 mm.
in length, but it is so poor that few reliable measurements can be
made.
The type of neither D. magnicornis nor D. limbatus is adequate
for accurate description, although Cope was able to report in con-
siderable detail on the latter. No skull is known for D. salaman-
droides, so that it cannot enter into the present discussion. My
attempts to find additional material at the type locality have met
with no success. The type of D. pusillus Broili, a very small skull,
was in the Munich collections. A small referred skull, A.M. 4523A,
figured by Case, has been available for study. There is every indica-
tion that this specimen at least is referable to Diplocaulus, although
Case and others have questioned this assignment, and that it is an
extremely immature specimen whose specific affinities are difficult
to determine.
This short account summarizes the principal contributions to the
taxonomy of the genus. Two species, D. limbatus Cope and D.
magnicornis Cope, have received rather widespread recognition.
D. copei Broili may be considered invalid, since the specimens upon
which the description was based cannot be distinguished from the
94 FIELDIANA: GEOLOGY, VOLUME 11
other Permian species. D. pusillus Broili has been held to be distinct
and questionably assigned to the genus Diplocaulus. D. primigenius
Mehl has received little attention since it was named. D. salaman-
droides, the type of the genus, is from an earlier (Late Pennsylvanian)
horizon than the Texas specimens. The material representing it is
unfortunately so incomplete that it cannot positively be stated on
the one hand that any Texas specimen differs from it specifically or,
on the other, that the Texas specimens are congeneric with it. The
most that can be said is that specific distinctions are likely on
stratigraphic grounds and that generic identity is not opposed by
the evidence available.
III. SPECIES AND GENUS
Various questions concerning the identity of several specimens
here included in the genus Diplocaulus have arisen in the past.
Williston (1918), for example, assigned U.C. 206 to a new genus,
an assignment supported by Case (1946) and others. Case (1911)
suggested that the smallest specimen, A.M. 4523A, might belong
to the Family Trimerorhachidae, and Douthitt (1917) likewise
believed that the specimen did not belong to the genus Diplocaulus.
Other specimens have been assigned to the genus only tentatively.
None of these investigators had access to a series including well-
distributed intermediate stages from the smallest to the largest
specimens. Now that such a series has been assembled it is possible
to make generic assignments with considerable confidence. There
are several pertinent items. Throughout the series the dermal bones
have similar mutual relationships and a common pattern not found
in any other recognized genus. The occiputs, palates and vertebrae,
so far as these have been observed, argue strongly for close relation-
ship. In all specimens the articulation of the skull and lower jaw
lies well forward on the lateral margin of the skull. In addition to
these general morphological similarities, the size distribution, based
on the midline length of the skull, shows no marked breaks in
continuity from the smallest to the largest specimen. There is
continuous and regular change in various characters throughout the
series. This will become more evident as regressions and ratios of
certain structures are considered. All these factors strongly suggest
a close relationship of all specimens included in the sample, a rela-
tionship that cannot be thought to transcend the generic level.
The problems of specific differentiation are treated first by
appropriate quantitative methods, followed by an analysis of generic
_ characters and comparisons of comparable characters of other genera
of amphibians.
SPECIES
Initial examination of the sample, as noted in the introductory
remarks, led me to believe that specific differentiation by inspection
95
96 FIELDIANA: GEOLOGY, VOLUME 11
was impossible, and thence I adopted as a working basis the hypoth-
esis that there was but a single species with a wide range in shape.
From a study of the initial twenty-four regressions, however, two
important concepts developed: one, that there were certain relation-
ships of skull parts that were constant throughout all specimens;
the other, that there were certain relationships that showed marked
deviations, with a tendency toward grouping, and that might serve
to differentiate the sample into two or more groups. Two of the
initial twenty-four tests gave particular promise in this direction,
Test 6, involving orbito-snout length, and Test 10, involving pre-
maxillary length. To these were added others not considered in
the preliminary analysis. The results of these studies are sum-
marized in the following paragraphs.
Analysis of Characters
ORBITO-SNOUT LENGTH: The suggestion that this might be a
significant measurement came from the regression of orbito-snout
length on skull length. The analysis, however, is based on ratios
of skull length to orbito-snout length (Table 5), since the figures
so obtained are more amenable to the types of study that must be
used.
TABLE 5.—RATIOS OF Ski/O-Si IN DIPLOCAULUS
Ski Ratio Ski Ratio Ski Ratio Ski Ratio
14 5.00 65 8.82 89 SESiT 114 4.38
19 5.00 68 4.00 89 4.64 114 4.22
23 5.75 70 8.89 95 2.92 115 4.11
24 4.52 75 3.95 97 3.88 118 4.07
81 8.88 75 3.26 101 4.02 119 4.41
50 SeaL 82 3.73 107 7.18 119 9.15
63 8.81 85 8.70 110 4.00 127 4.10
136 7.56
TABLE 6.—FREQUENCY DISTRIBUTION OF Ski/O-Si IN DIPLOCAULUS
Class No. Class No. Class No.
2.50-2.99 1 5.00-5.49 2 7.50-7.99 1
3.00-8.49 1 5.50-5.99 iL 8.00-8.49 0
3.50-3.99 10 6.00-6.49 0 8.50-8.99 0
4.00-4.49 9 6.50-6.99 0 9.00-9.49 1
4.50-4.99 2 7.00—-7.49 1
Table 6 suggests two groups with discontinuous distribution, one
containing twenty-six specimens and the other but three. The three
with high ratios are U.C. 1661 and 1648 and A.M. 4470. It should
be noted that there is a negative correlation of the ratio of skull
length and orbito-snout length on skull length and that values in
OLSON: DIPLOCAULUS 97
excess of 5.00, except for the three specimens cited, occur in skulls
less than 24 mm. in length.
A second approach, which is suggestive but not definitive, is
through use of the coefficient of variability (V). This must be
based, of course, on the ratios and not on direct linear measurements
and so is not commensurate with values derived from linear measure-
ments and cannot be compared with such values in estimating real
variability. The symbol Vp is used for the coefficient based on ratios.
The value thus derived may have meaning, however, if compared
with results obtained by similar treatment of data from other sources.
In this instance the coefficient of variability derived from ratios is
29.2 from the equation
Vr=1.325X100/4.5593
The value of Vz from a sample of 104 specimens of Bufo marinus,
a species that shows a coefficient of variability of 10.0 in orbito-
snout length based on linear measurements of adults, has a value
of 18.8 for Vp, determined on the basis of the whole sample, using
the ratio of skull length to orbito-snout length as in Diplocaulus.
The sample of Bufo marinus is comparable in essentially all respects
to that of Diplocaulus, consisting of immature and mature individuals
and having been collected over a relatively wide area. The value
18.8 is decidedly lower than the 29.2 of Diplocaulus in spite of the
fact that the coefficient of variability (V=10) is moderately high.
There is some indication from this comparison that the sample of
Diplocaulus may not be pure. An alternative explanation might
be that Diplocaulus, assuming a single species, is excessively variable
in the relationship tested; variability to the extent implied, however,
is sufficiently rare to be improbable.
LENGTH OF THE PREMAXILLARY: The premaxillary enters into
the formation of the preorbital region of the skull along with the
frontal bone. Since it has been shown in the initial tests that the
frontal length in relationship to skull length is moderately constant
in the genus, it might be expected that the shortness of the snout in
the three specimens separated from the rest in the preceding para-
graph would result primarily from shortness of the premaxillary.
Were this the case, the relationships of this bone should provide a
particularly sensitive test. Part of the shortness of the snout,
however, involves the relative position of the orbits and the frontals
so that the premaxillary is not as effective a basis for differentiation
as might be thought. Ratios for this relationship are given in Table 7.
98 FIELDIANA: GEOLOGY, VOLUME 11
TABLE 7.—RATIOS OF Ski/Pmzi IN DIPLOCAULUS
Ski Ratio Ski Ratio Ski Ratio Ski Ratio
14 28.0 70 APART 98 Loco 119 eS
2a ea) 15 LOT 101 1 BS BAA 119 papa ass
31 LAT 80 8.9 107 2987, 136 Zot
50 10.4 82 9.9 110 110
63 LD 85 10.5 114 O38
65 10.0 89 10.9 114 13.4
65 10.8 95 7.9 115 OFT.
68 TsO 97 10.0 118 a Ee
TABLE 8.—FREQUENCY DISTRIBUTION OF Ski/Pmxi IN DIPLOCAULUS
Class No. Class No. Class No.
7.0-8.9 2 15.0-16.9 i 23 .0-24.9 L
9:0-10.9 10 17.0-18.9 0 25.0-26.9 0
11.0-12.9 6 19.0-20.9 0 27 .0-28.9 if!
13.0-14.9 3 21.0-22.9 2 29 .0-30.9 1
The frequency distribution based on ratios of skull length to
premaxillary length (Table 8) suggests the presence of two groups,
using a class interval of 2, but the meaning is somewhat clouded,
for the group of five specimens in classes 21.0-22.9 to 29.0-30.9
includes specimens U.C. 1661, U.C. 1648, A.M. 4470, A.M. 4523A
and U.C. 206. The first three are large, 107 mm. or more in length,
and the last two are very small, 14 and 23 mm., respectively. The
two small skulls were included in the large suite of specimens differ-
entiated by the orbito-snout length, while the three large skulls
composed the small group. Placement of the small skulls on the
basis of the premaxillary is less certain. There are two possibilities:
that the small skulls actually belong to the group with which the
ratios associate them, or that they pertain to the other group but
are separated from it on the basis of ratios that result from differences
between adults and juveniles. The scatter diagram (fig. 16) points
the way to the most logical explanation.
On the basis of the distribution, the two small skulls could have
been modified to give rise to either pattern in the large skulls. If
they gave rise to the three large skulls with very high ratios, little
change in ratio with increase in skull size occurred. But if this was
the case, it must be assumed that the sampling, which was random,
produced two very small and three large members of this group but
failed to produce any intermediate-sized specimens. This is possible
but seems improbable on ecological grounds, as discussed on pages
104-110. There can be little doubt that the three large skulls, U.C.
1661 and 1648 and A.M. 4470, differ significantly in this character
from other large skulls. The contention that the two small skulls
OLSON: DIPLOCAULUS 99
actually pertain to the larger suite of specimens and that there was
a very rapid change in proportion with increase in skull length is
supported by the distribution on the scatter diagram and by dis-
tributions based on other characters. Results based on the pre-
maxillary cannot be considered definitive when applied to the smallest
skulls but the character is of great significance among large specimens.
4
fe] ra
30 re) ©
SK, ° oo
eae
PMX
| [e} °
10 b QoP ° rel & °%
4 _ (> By A OY
° 10 20 30 40 50 60 70 80 90 100 WO 120 130 140 150
SK,
Fic. 16. Scatter diagram of ratios of Ski/Pmzi on Ski.
Blind adherence to a single quantitative test in this instance would
appear to lead to an improper conclusion.
POSTERIOR CURVATURE OF THE SKULL: It was believed, as pre-
liminary analyses were being carried out, that the nature of the
posterior curvature would prove to be useful. It is evident that
there is considerable difference in the curvature in large skulls
(cf. pls. 4-7). It is possible to devise various measurements that
will express these differences quantitatively, and several have been
used. For Test 14 the following system was used to give a single
value that expressed the nature of the curve as desired for our pur-
poses. A line, designated as the X-axis, was projected posteriorly
from the midline termination of the skull as a continuation of the
midline for the distance of one-half the skull length. A second
line, the Y-axis, was constructed normal to X and projected to the
level of the horn on either side. This line was then divided into
ten equal parts between the midline and the level of intersection
with the horn. Using all specimens, N=32, a mean value for X,
the distance from the posterior margin of the skull to the line Y,
was determined for each value of Y; that is, Y=0 at intersection of
lines X and Y, Y=1, Y=2, ete. Deviations of X for each specimen
at levels of Y=0 to 9 were determined and these were totaled and
divided to give a mean deviation of X, Mdz, for each specimen.
Various other methods were used as well, but the results in all
100 FIELDIANA: GEOLOGY, VOLUME 11
lacked definition and for the most part failed to express conditions
as well as the one outlined above.
The results in Test 14 were not clearly definitive, so that the
details of the test are not included. If skulls measuring more than
100 mm. only are used, two groups are clearly defined, one consisting
of U.C. 1661, 1655 and 1648 and A.M. 4470, and the other including
the remainder of the skulls over 100 mm. Posterior curvature will
not, however, isolate partially grown skulls from the adults of either
group, for the partially grown specimens are somewhat intermediate
between the two groups in this character.
HorRN LENGTH: Horn length as used in this paper refers to the
distance from the level of the posterior termination of the midline
of the skull to the tip of the horn, measured parallel to the midline.
This measurement is strongly modified with change in skull size and
relative growth is distinctly heterogonic. This poses some difficulties
in differentiation of species. This characteristic is, of course, reflected
in the ratios of Skj to horn length (Hj), Table 9.
TABLE 9.—RATIOS OF Ski/Hi IN DIPLOCAULUS
Ski Ratio Ski Ratio Ski Ratio
23 6.71 89 Bea! 118 1.31
81 2.82 98 1.88 119 0.88
65 Lt 101 1.58 119 1.59
65 2.50 105 2.19 120 0.86
68 2.06 107 0.82 127 1.55
70 1.94 110 162 136 0.97
85 ya 4 114 1.52
The frequency distribution of the ratios (Table 10) shows a
decidedly skewed pattern, since there is a strong positive heterogony
in relative growth of horn length in relationship to skull length that
is evident in the ratios. In spite of this fact, three specimens, which
have been separated on other bases, U.C. 1661 and 1648 and A.M.
4470, appear to be definitely distinct from the remainder, except
for U.C. 1655, a specimen that has not entered into any of the
previous determinations. If only skulls measuring over 100 mm.
are used, and a smaller class interval than is practical for the whole
TABLE 10.—FREQUENCY DISTRIBUTION OF Ski/Hi IN DIPLOCAULUS
Class! No. Class No. Class No.
0.75-0.99 4 1.50-1.74 6 2.25-2.49 iL
1.00-1.24 0 1.75-1.99 2 2.50-2.74 i)
1.25-1.49 1 2.00-2.24 3 2.75-2.99 1
1 Value for skull of 23 mm. length, 5.71, falls in class 5.50—-5.74. This is not
entered in the table since it extends tabulation unnecessarily.
OLSON: DIPLOCAULUS 101
sample is used, separation into two groups is clear. Evidence for
the sample as a whole is apparent from study of the relationships
shown when the ratios are entered against skull length on double
logarithmic paper (fig. 17). The isolation of the four specimens is
evident and there are no specimens clearly intermediate between
them and the smallest skulls. The remainder, on the contrary,
appear to form an integrated pattern that would be expected in
°
Ny)
ad
o
10 20 30 40 60 80 100 140
SK,
Fic. 17. Scatter diagram of ratios of Ski/Hi on Ski.
view of the nature of skull changes. This by no means precludes
the possibility that the smallest skulls could represent growth stages
of the group represented by the four large skulls, but it suggests
that this was not the case. As was pointed out in the instance of
premaxillary length, the ecological situation has an important bear-
ing on this matter.
NATURE OF THE PARIETAL: The parietal bones seem to show
considerable variation in a number of features within the genus,
but linear measurements or ratios do not differentiate groups. There
is, however, one feature, not readily amenable to measurement, that
is important. The dorsal surface of the parietal, particularly of
the distal end, assumes two distinct patterns. It is either essentially
flat, or it is convex dorsally. Convexity appears in four skulls,
102 FIELDIANA: GEOLOGY, VOLUME 11
U.C. 1648, 1655, and 1661 and A.M. 4470. This character may be
one that does not occur in immature specimens and, although it
separates mature skulls into two groups, it may be valueless for very
small skulls. From the nature of development of the parietal it
appears most probable that the convexity would be evident, in the
group in which it appears, by the time the 60 mm. stage of skull
length was reached. There is no evidence of it in any skulls over
this length except in the four cited.
THE BEARING OF POSTCRANIAL FEATURES: It is reasonable to
suppose that differences of sufficient magnitude to allow separation
of groups might be present in the postcranial skeleton of Diplocaulus,
but the generally fragmentary nature of the postcranium in the
majority of specimens has made studies of most elements difficult.
With the known material, only the vertebrae appear to offer any
possibility of fruitful study. The vertebrae of only twelve of the
100 specimens available can be used for comparisons. This results
from incompleteness of the columns associated with the skulls,
disarticulation of the vertebrae, which makes it impossible to
determine their position in the column, and the fact that, although
vertebrae are abundant in deposits in which skulls are known,
associations of skulls and vertebrae are not common. Only crude
quantitative methods can be used. Major differences between
vertebrae associated with skulls that are very similar render the
available data inadequate for the formulation of reliable conclusions.
The real problem in consideration of the vertebrae is whether or
not observed differences have any real taxonomic significance. One
species, D. primigenius Mehl, has been described on the basis of
vertebral structure. The vertebrae in the type, U.C. 564, are
certainly atypical in size and in development of the neural spine,
but they are almost identical in both respects with the vertebrae
associated with the skull of A.M. 4470. U.C. 564 and A.M. 4470
are very different in skull structure and consistently fall into different
groups on the basis of skull features. The vertebrae are unknown
in other specimens of the group to which A.M. 4470 belongs. Thus
the question of the relative value of vertebral and skull patterns
arises.
Measurements of the centra along the ventral midline of the
sixth vertebra posterior to the occipital condyle are given in Table 11.
This particular vertebra was selected, since it could be identified
in the largest number of specimens. In the table, skull lengths are
grouped on the basis of 10 mm. class intervals and the midpoint of
OLSON: DIPLOCAULUS 103
each class is used for determining ratios. Grouping was used because
estimates of skull lengths were necessary for some specimens.
TABLE 11.—LINEAR MEASUREMENTS AND RATIO V1/Ski IN DIPLOCAULUS
Specimen
Number Ski Vii Ratio V1/Ski
SM AAG Si eS tee eet, 60-69 15 0.23
WiC S1GbSet een eee 60-69 11 0.17
ECG HO aoe eee es re 80-89 17 0.20
LOU Gea 0 SS aa oe Os ae 90-99 18 0.19
MEG, Dake ee oo A atte 90-99 16 O17
WC OLS eee ear 100-109 25 0.17
AM AATS ee ae ee ne 110-119 30 0.22
WiC bGA PN A ae oe ee 110-119 33 0.26
ROM ARTO oo i eerie a ot 110-119 23 0.29
AM AAT Oe he eee Roe 120-129 25 0.18
BM AER E oy aN! 140-149 25 O17.
1 Vj=length of sixth vertebra.
The mean value of the ratios is 0.204. Distribution around the
mean shows no significant relationship to skull size. There is, of
course, some correlation of skull length and vertebral length. It is
possible that distribution determined from an adequate sample would
show some integrated pattern of relationship of the vertebral and
skull characters. There is, however, no indication of the sort of
separation that would be expected were the proportional differences
significant as group characters. Additional support of this concept
is afforded by the lack of correlation of vertebral and skull differences
as shown in the similarities of the vertebrae and the major differences
in the skulls of A.M. 4470 and U.C. 564.
Evidence bearing on the causes of differences in vertebrae is
slight. As will be shown later, in discussions of the growth of the
skulls, certain patterns may be interpreted as resulting from the
retention of youthful features of form in large skulls, a possible in-
dication that some factor or factors tending to retard attainment of
complete maturity were active. If we assume that the vertebrae of
U.C. 564 and A.M. 4470 have fully attained the adult condition,
it is apparent that the vertebrae of the other large specimens have
failed to attain this status in either size or form. The degree of
maturity, if this be the explanation, varies widely in different in-
dividuals of approximately the same skull length. A most interesting
implication, borne out by specimens with almost complete series of
vertebrae, is that there was a marked difference in total body length
in specimens with approximately the same skull length. Were a
large series of specimens with well-preserved skulls and vertebral
columns available, it might be possible to recognize concurrent im-
104 FIELDIANA: GEOLOGY, VOLUME 11
maturity of vertebrae and skulls in individuals. The material at
hand gives no suggestion of such a correlation.
In summary, the following may be said: There is no positive
evidence that vertebral characters can be used for specific differentia-
tion. Vertebral variation in length and shape may be due to some
factor or factors that acted to retard maturation of the skeleton,
but as yet the evidence is merely suggestive.
The Bearing of Ecological Considerations on Group Differentiation
The use of the term species has been carefully avoided to this
point in the discussion. We have been able to differentiate struc-
turally two groups of Diplocaulus, one composed of a large number
of specimens and one of very few. As yet the nature of this difference
has not been discussed, since this would have clouded the issue of
its mere existence. The two groups might represent two species or
might represent the two sexes of one species. In the present section,
until this matter has been considered fully, we will designate the
group with the majority of individuals as A and that with the smaller
number, including U.C. 1661, 1655 and 1648 and A.M. 4470, as B.
The mode of occurrence of the specimens in the deposits and the
interpretation of their former environment have an important bearing
upon the interpretation of the two groups and upon reference of the
smallest skulls in the sample to one or the other. Evidence of this
sort, being in part conjectural and in part dependent upon negative
evidence, cannot be conclusive in itself. Taken in conjunction with
the morphological indications outlined in the preceding paragraphs,
however, it does assume real meaning.
All specimens have come from the Arroyo Formation of the Clear
Fork Group. Vertebrates occur under a wide variety of circum-
stances in these beds. A brief review of the nature of occurrences
and assemblages is necessary to an understanding of the place of
Diplocaulus in the fauna.
The Arroyo deposits in Baylor and Wilbarger Counties, Texas,
from which the sample was drawn, overlie the marine Lueders
limestone but are themselves entirely non-marine in origin. Red
clays and sandstones predominate in the exposures in the valley of
the Wichita River. In a few places, particularly in the easternmost
exposures of the formation, gray and greenish-gray clays occur.
Local transitions from red to green are characteristic of both the clays
and the sandstones throughout the area. The sandstones occur in
broad sheets and as linear deposits with widths seldom exceeding
OLSON: DIPLOCAULUS 105
fifty feet. At various places the linear sandstones grade into fine
conglomerates. Over very limited areas, the crossbedding of the
sandstones suggests aeolian origin. There is a gentle regional dip
to the west in the area, but locally dips, up to about 10 degrees,
are random in their orientation. The varied nature of the sediments
and irregularities of local structure make it virtually impossible to
do detailed stratigraphic studies.
Many specimens of vertebrates occur in the widespread, relatively
homogeneous red clays. These clays appear to have been deposited
for the most part on flood plains marginal to the streams. Wide
expanses of the clays are barren of fossils, some carry scattered,
usually disarticulated specimens, and in a few places there are con-
centrations of well-preserved skeletons, which, under particularly
favorable circumstances, may form bone beds. It appears that these
concentrations, which have yielded most of the good Arroyo speci-
mens, represent deposits in ponds and ox-bows that. lay marginal
to the channels of the streams. The ‘“Labidosaurus Pocket’ in
Baylor County, Texas, located by aerial photographs on CUM 8B
65, 7.38-1.1,! is one such case. The assemblage, as I have observed
it, consists of Dimetrodon, Edaphosaurus, Captorhinus, Seymouria,
unidentified small forms, and Diplocaulus. Another example of such
an occurrence is the ‘‘Broiliellus Pocket,’’ CUM 8B 6, 4.4-7.4,
which has yielded Dimetrodon, Edaphosaurus, Captorhinus, Sey-
mouria, Eryops, Trematops, Broiliellus, an undetermined genus of
Dissorophidae, Diplocaulus, and Xenacanthus. A notable point con-
cerning such localized assemblages is that the adjacent clays, very
similar in appearance, are for the most part barren. Specimens that
do occur in adjacent deposits usually consist of isolated bones or
badly scattered partial skeletons. Presumably, they were buried
some time after death occurred, perhaps during flood stages of the
streams, after considerable disarticulation by carnivore action,
decomposition, and water action.
An assemblage rather different from these concentrations in the
red clays is present in the “Lysorophus Pockets” (Olson, 1939),
which also occur in the clays but contain nodular masses with
Lysorophus, small gymnarthrids, Diplocaulus, and occasional scraps
of large tetrapods. Probably these also represent ponds, possibly dry-
ing ponds, in which small amphibians sought refuge by burrowing.
Another type of clay deposit consists of light-colored, homoge-
neous, gray clay. This type, which is commonly limited in extent,
1See E. C. Olson (1948) for use of this index system.
106 FIELDIANA: GEOLOGY, VOLUME 11
is more abundant in the Upper Clyde than in the Arroyo, but it does
occur near the base of the Arroyo in the vicinity of Grey and Pony
creeks. In such deposits occur fragmentary remains of carbonized
plants, some gypsum crystals, and small concentrations of copper-
bearing minerals. From the Upper Clyde, CUM 2B 150, around 3.4—
2.6, the following vertebrate assemblage has been observed: Dimet-
rodon, Ophiacodon, Captorhinus, Diadectes, Trimerorhachis, Eryops,
Archeria, and Xenacanthus. Diplocaulus has not been noted here
but it does occur in the Grey Creek and Pony Creek localities in
the Arroyo, under somewhat similar circumstances. The highly
leached, reduced, underclay-like beds in these localities suggest
deposition under swamp conditions.
The sandstone deposits appear to have been formed under a
variety of circumstances, the majority as moderately widespread
sheets on flood plains. They are moderately even-bedded, con-
tinuous laterally, little varied in dip, and nearly unfossiliferous. The
very few vertebrates found in them are usually fragmentary; in
only one instance have I encountered complete skeletons, these
being a “nest” of three specimens of Seymouria in an extensive,
ridge-forming sandstone along the western margin of Brushy Creek,
Baylor County, Texas. Argillaceous sandstones, apparently also
of flood plain origin, are usually mud-cracked and carry tracks of
vertebrates and invertebrates. A few instances of windblown sands
have been observed, but they are uncommon and completely barren
of fossils.
In some places, for example in an area about one-half mile north
of the “Labidosaurus Pocket,’’ CUM 3B 64, 7.8-5.8, the sandstones
are linear in outcrop and highly varied in dip over very short dis-
tances. In the area cited, linear deposits of sandstone with strikes
of about N. 60° W. crop out over a considerable area. They show
rapid changes in dip, and the sands grade into fine conglomerates
at various places. The pattern and the distribution of particles
suggest that the deposits were made in stream channels during times
of vigorous water flow. It seems probable that the streams were
intermittent, dry during part of the year and actively flowing over
moderately extended periods. Fossil vertebrates occur sporadically
in such sandstones and are usually fragmentary. Dvimetrodon,
Edaphosaurus, Captorhinus, Diplocaulus, and Xenacanthus have
been recorded from the locality cited.
Certain of the fine conglomerates found in the Arroyo are also
presumably of channel origin. There are widespread sheet con-
OLSON: DIPLOCAULUS 107
glomerates, which appear to be of flood plain origin, but they are
rare and seldom fossiliferous. Many of the dark brown, fine con-
glomerates exhibit linear patterns suggestive of channel origin, and
occasional junctions of two such deposits, plus a random orientation
over limited areas, are interpreted as evidence that the small channels
formed part of anastomosing or braided streams. As in the case
of the channel sandstone deposits, the conglomerates appear to have
been deposited under conditions of alternating wet and dry seasons.
A wide variety of vertebrates, mostly fragmentary, have been ob-
tained from the conglomerates: Dimetrodon, Edaphosaurus, Diadectes,
Captorhinus, Seymouria, Trematops, Trimerorhachis, Dissorophus,
Diplocaulus, and Xenacanthus. By far the most abundant are teeth
of Xenacanthus and scraps of skulls, vertebrae, and girdles of
Diplocaulus.
This survey of types of occurrences, assemblages, and the general
life environment of Arroyo vertebrates is important for an evalua-
tion of the conditions under which Diplocaulus lived, and this, in
turn, is important in an evaluation of the nature of the differences
between the two groups of Diplocaulus. It can hardly be denied
that Diplocaulus was totally aquatic. Although it is recorded from
all types of deposits, it is rarely found in those that can be interpreted
as originating on flood plains. It is usually considered to have been
a somewhat sluggish swimmer, a bottom-living animal that fed on
soft foodstuffs, perhaps plants and small invertebrates. The function
of the postero-lateral projections of the skull—the horns—is con-
jectural. It has been supposed that they supported lateral flaps of
skin used for swimming in a skate-like fashion. The tail, which is
poorly known, was believed by Douthitt (1917) to have been long
and tapering, a view based on inconclusive evidence, although a
whiplash tail and paired lateral flaps do occur together in a number
of aquatic vertebrates. It is interesting to note, however, that it is
not until the 100 mm. stage in skull length is reached that excessive
breadth of skull is attained; any lateral fin-like structures could
hardly have had an important function prior to this stage. No
traces of them have ever been found, even in very fine sediments,
and the posterior margin of the skull shows no markings that might
be associated with such structures. Evidence concerning the presence
of lateral flaps is therefore inconclusive, to say the least. The
broad skull may well have served some entirely different function
than a flap support, even, perhaps, one of aiding in working into
sand or mud for protection from predators or during periods of dry
weather.
108 FIELDIANA: GEOLOGY, VOLUME 11
The distribution of Groups A and B relative to the types of sedi-
ments in the area is of importance. Members of Group A have been
found preserved under a wide variety of conditions, in pond deposits
and swamp deposits and also in the sandstones and gravels of channel
origin. On the other hand, the specimens that can definitely be
referred to Group B all came from channel deposits. U.C. 1661
and 1648 were found in coarse sandstone deposited in stream channels.
On the basis of the matrix U.C. 1655 and A.M. 4470 appear to
have come from conglomeratic channel deposits. Extensive field
work and studies of museum collections have revealed no evidence
of occurrence of specimens with the characteristics of Group B out-
side of channel deposits. There is an association of specimens of
Groups A and B in only one instance. No specimen with a skull
length under 60 mm. has been found in the channel deposits, but this
- is probably a matter of poor preservation under turbulent conditions,
for fragments of small plates and vertebrae have been found.
The conclusions that can be drawn from these ecological con-
siderations, while inevitably based in part on negative evidence,
nevertheless appear to be significant in their bearing upon the related
questions of the assignment of small specimens to Group A or B
and the meaning of the differentiation of the two groups.
It has been seen that the relationships of the orbito-snout length
and skull length point strongly toward an association of the very
small skulls with the larger specimens that may definitely be assigned
to Group A. The other characters based on linear measurements
are less definite in this respect, although in each instance reference
of the small skulls to Group A seems the more logical deduction.
The same applies to the nature of the dorsal surface of the parietal.
The parietal and the premaxillary show, with little doubt, that all
specimens with skull length 60 mm. or greater, except for the four
that compose Group B, must be referred to Group A. It is, thus,
only for skulls under 60 mm. in length that any doubt exists. All
of these have come from clay deposits.
If it be assumed that any or all of these pertain to Group B, it
follows that the immature stages of this group were spent in ponds
and swamps. This is not impossible, but in order to bring it about
the adults would have had to penetrate these breeding grounds.
The death of many and the subsequent preservation of some would
surely have been inevitable, yet no trace of an adult resembling the
members of Group B has been found in the clays. We might assume,
however, that only the females penetrated the still waters and that
OLSON: DIPLOCAULUS 109
Group A represents the females and Group B the males. This
assumption presupposes that internal fertilization occurred within
the group, in contrast to the mode of fertilization in extant am-
phibians. Even if the possibility of internal fertilization is granted,
there remains the serious difficulty that the males, but not the
females, must have left the environment in which the eggs were
laid prior to reaching the 60 mm. stage, at which time the males
would have been little differentiated functionally from the females
if the pattern suggested by the small skulls be taken as a criterion
for interpretation of the growth pattern. It also becomes necessary
to explain the absence of 60 to 100 mm. males in deposits laid down
in stream channels in which skulls of not much more than 60 mm. in
length are preserved.
The continuity of sizes and form of skulls in the clay deposits
and the absence in the clay and in deposits formed in stream channels
of any skulls of Group B between 60 and 100 mm. in length, strongly
imply that all specimens in the clay belong® to Group A. The
difficulty of assuming the two groups to represent males and females
of the same species is accentuated by the disparity in numbers. Of
perhaps thirty-five specimens that have come from sediments
deposited in channels, only four can be assigned to Group B.
The total effect of differences in single skull characters upon
skull shape and the dynamics of the skull as a leading structure in
swimming also contribute something to the interpretation. Adult
skulls in Group A are broad, flat, and relatively thin-boned, and
hence poorly adapted, it would seem, to life in turbulent running
water. The orbito-snout region is moderately long, and the eyes,
which are thus well back on the skull, are directed dorsally, as in
many bottom-living animals. The adult skulls in Group B, however,
are moderately stream-lined, being narrower posteriorly, with long,
posteriorly directed, tapering horns. The bone is thicker and the
skulls appear to be somewhat deeper. The orbito-snout length is
short, compared to that in Group A, and the eyes, lying closer to
the tip of the snout, appear to have been directed somewhat forward.
This would be expected in a more actively swimming animal. We
seem to see, then, a contrast in adaptation, one to life in ponds
and swamps and the other to life in rivers and streams. The occur-
rence of representatives of the first type in channel deposits may
well be attributed to floods that swept them from their normal
environments into streams, together with large reptiles and more
_ strictly terrestrial amphibians, remains of which also occur in channel
110 FIELDIANA: GEOLOGY, VOLUME 11
deposits. There is in these observations evidence of a real ecological
separation that supports a view that the two groups differ specifically.
In summary we may draw the following conclusions: Groups A
and B represent different species. Group A inhabited ponds and
swamps, while Group B lived in running water. Group A bred in
the area from which the collections have been made, but Group B
penetrated the area only during time of high water, following active
streams, and presumably bred elsewhere.
Taxonomy
There appear, therefore, to be two recognizable species of the
genus Diplocaulus in the Arroyo Formation, differing in morpho-
logical characters and, apparently, in habitat and adaptations as
well. One comprises four individuals in the sample studied and the
other the remainder.
The only questign remaining is the relation that the various
named species bear to these two groups. D. magnicornis Cope is
the first described Permian species. The skull of the specimen,
A.M. 4539, upon which the type description was based,! although
poor, is clearly a member of the larger series, Series A of the foregoing
discussion. This name clearly applies, therefore, to this suite of
specimens. The types of D. primigenius Mehl and of Permoplatyops
parvus (Williston) and the referred specimen of D. pusillus Broili
(the type of which was lost long ago) are, as shown above, members
of the same series and accordingly fall into the synonymy of D.
magnicornis. This is also true of D. limbatus Cope. D. coper Broili
may be rejected as indeterminate, as shown by Case (1911).
Diplocaulus magnicornis Cope
Diplocaulus magnicornis Cope, Proc. Amer. Phil. Soc., 20, p. 458, 1882.
Diplocaulus limbatus Cope, Proc. Amer. Phil. Soc., 34, p. 456, 1895.
Diplocaulus pusillus Broili, Paleontographica, 51, p. 24, 1904.
Diplocaulus primigenius Mehl, Jour. Geol., 29, pp. 48-56, 1921.
Permoplatyops parvus Williston, Contr. Walker Mus., 2, p. 110, 1918.
1JTn addition to the skull, A.M. 4539 formerly included scraps of other, speci-
fically indeterminable skulls, two atlases, two axes, sixteen other complete verte-
brae, interclavicle and clavicles and fragments of ribs. The association of these
various parts is open to question. An atlas and axis and the third and fourth
vertebrae, which are clearly associated with the skull, were described in detail by
Cope. The remainder of the specimen, except for the skull, were, strictly speaking,
cotypes. To stabilize matters, the skull, atlas and axis and third and fourth
vertebrae are here formally designated as the lectotype. The remaining material
has been recatalogued as A.M. 4539A.
OLSON: DIPLOCAULUS 111
Type (lectotype): A.M. No. 4539. Skull and four anterior
vertebrae from Coffee Creek, Baylor County, Texas.
Hypodigm: Type and A.M. 4466, 4467, 4468, 4469, 4471 (type
of D. limbatus),! 4472, 4473, 4478, 4494, 4498, 4501, 4504, 4509,
4511, 4514, 4523A, 4523B, 4527, 4528, 4530, 4538, 4543, 4589, 4597,
4742. C.N.H.M.-U.C. 206 (type of P. parvus), 207, 221, 222, 223,
229, 410, 564 (type of D. primigenius), 636, 637, 1018, 13817, 1650,
1652, 1658, 1654, 1656, 1657, 1658, 1660, 1668, P12689. U.S.N.M.
17884.
Horizon: Arroyo Formation, Clear Fork Group, Early Permian.
Diagnosis: Skull length less than five times orbito-snout length
and less than sixteen times premaxillary length. Skull length greater
than horn length. Surface of parietal bone flat, not convex dorsally.
Remarks: The characters cited in the diagnosis will separate skulls
of adult members of this species from those of the other. It is im-
possible to know whether each would distinguish very small skulls,
for no comparable specimens of Series B are available to make the
necessary tests. It seems highly probable that the relationship of
skull length and orbito-snout length would prove definitive. Were
it possible to obtain a large representation of the two species in the
very small size groups, separation might be made by quantitative
studies, but it is improbable that adequate collections will ever be
available. The character of the parietal surface almost certainly
would not be definitive below a skull length of 50 or 60 mm. The
small specimens, those under 60 mm., have been referred to D.
magnicornis in the present paper on the bases of the relationship
of the skull and orbito-snout length, of their apparent association
with the adults of the species in various regression patterns, and of
ecology.
The regression lines for characters analyzed in the two species
would almost certainly prove to be significantly different could
comparisons be made, but no regression lines for the second species
can be determined.
The other species of Diplocaulus, Series B, present a less simple
case. A specimen referred to D. limbatus Cope by Case and used
as the basis for the revised description, A.M. 4470, is a member of
this species. The type of D. limbatus, A.M. 4471, must be referred,
as noted, to D. magnicornis on the basis of the orbito-snout length,
1 This specimen does not appear in the tables. It is poorly preserved, but the
orbito-snout length is measurable and indicates clearly that it belongs to this series.
112 FIELDIANA: GEOLOGY, VOLUME 11
one of the few observable characters. A new species must, there-
fore, be erected for the four specimens in Series B. This may be
defined as:
Diplocaulus brevirostris sp. nov.
Type: A.M. 4470, skull, vertebrae, and parts of appendicular
skeleton. Coffee Creek, Baylor County, Texas. Collected by C.
Sternberg, 1896.
Hypodigm: The type and A.M. 4544,! C.N.H.M.-U.C. 1648,
1655, 1661.
Horizon: Arroyo Formation, Clear Fork Group, Early Permian.
Diagnosis: Skull length at least seven times preorbital length.
Skull length more than twenty-one times length of premaxillary.
Horn length greater than skull length. Dorsal surface of parietal
strongly convex dorsally.
Remarks: The listed characters apply to adults only, for the
young stages of this species are unknown. The smallest known
individual has a skull length of 107 mm. The nature of the posterior
curvature of the skull will differentiate adults of this species from
those of D. magnicornis, but it may be noted in plates 1-5 that the
pattern of curvature in specimens of D. magnicornis of less than
100 mm. skull length, as well as that in A.M. 4514, approaches more
closely the curvature in D. brevirostris than that in the larger skulls
of the species to which they belong. If, however, the regression of
horn length and a coefficient of curvature are studied on the basis
of the whole sample, a separation of the two species is apparent.
The skulls referred to D. brevirostris are distinctly mature, the bones
are heavy, and the pitting of the dermal surface is highly developed.
A basis for specific differentiation may lie in the degree of maturity
attained and in the stage at which it is attained, but the sample of
D. brevirostris is not large enough to more than suggest the possibility.
Only one specimen of D. brevirostris, A.M. 4470, has associated
vertebrae. These are large, mature, and very similar to those of
C.N.H.M.-U.C. 564. At present there is no basis for separating
the two species on vertebral characters.
1 This specimen has not figured in the calculations and discussions. It was
but recently identified as a member of the species in re-examination of fragmentary
materials. Skull length is not available, but the short orbito-snout length is clear
indication of its taxonomic position. This specimen, like the other four, was found
in conglomerate. It, therefore, adds some strength to the arguments on ecology
presented in earlier pages of the paper.
OLSON: DIPLOCAULUS 113
GENUS
Introduction and Methods
In the preliminary crude analyses it was apparent that certain
regressions showed a close grouping of points around the regression
lines, that is, correlation appeared to be very high, and offered no
evidence to suggest that the sample was not homogeneous. These
relationships involved the regressions of interorbital width, frontal
length, parietal length and interparietal length on skull length. Other
regressions, as noted, suggested that two groups might be present;
still others showed such a wide scattering of points that their value
in taxonomic work, in view of the size of the sample, was questionable.
In the present section attention will be focused on the four
measurements that appear to be common to the genus as it is now
understood and do not reflect species differences. The mere fact
that these relationships are common to the genus in no way implies
that they may not be common to other genera as well. They do,
however, seem to offer possibilities for generic differentiation and
one of the principal functions of this section is to study these relation-
ships and their utility in taxonomic work.
Throughout the remainder of this section the genus will be con-
sidered as a unit and comparisons will be made with other genera
treated in like manner. This practice affords an approach to the
practical matter of differentiation of genera by applications of
methods essentially the same as those usually applied to species.
It does not imply that genera and species are considered as com-
mensurate units. The samples of genera that have been used have
not, of course, been drawn from populations in the strict biological
sense of the word but are representative of populations in the
statistical sense. It is necessary to analyze patterns of relative
growth in various phases of the work. In such instances reference
is made to growth patterns of the genus in question. Such patterns
represent an estimate based on stages of growth of individuals of
the included species of a genus just as the relative growth patterns
determined for a single species represent an estimate based on a
sample of individuals of that species.
The practical effect of using the genus rather than the species
as a unit is, in most cases, to increase the dispersal of values, around
a mean or a regression line, as the case may be, over that which ob-
tains within a single species of the genus. In the case of the four
measurements used in this study, however, dispersal has not been
increased over that determined for D. magnicornis alone by inclusion
114 FIELDIANA: GEOLOGY, VOLUME 11
of specimens of D. brevirostris in the sample. It is possible, although
improbable, that addition of smaller specimens of D. brevirostris
would result in a significant modification. The effect of the presence
of more than one species in the sample of Trimerorhachis, which is
used for comparison, cannot be evaluated from the material available,
but this is unimportant for present considerations, since our purpose
is to treat the genus as a whole.
There is no difficulty in differentiating moderately well-preserved
mature skulls of the genus Diplocaulus from those of any other known
genus. The characters listed in Case’s redefinition of the genus
(1911) are sufficient for this purpose. That this sort of evaluation is
not entirely satisfactory, however, is shown by the confusion that
has arisen a number of times in generic assignment of small skulls
and poorly preserved or unprepared larger skulls. Small skulls,
now known to belong to the genus, have been referred variously to
the families Trimerorhachidae and Gymnarthridae. It is to such
cases particularly that quantitative methods, especially those in-
volving the most commonly preserved part of the skulls, the central
portion, can apply. Thus, if it can be shown that the four features
that have been mentioned as being stable within the genus, differ
from the same features in those genera that may be confused with
Diplocaulus, an important step in taxonomic work will have been
made.
To test the utility of the four relationships for this purpose, a
series of samples of definitely identified specimens of Late Paleozoic
amphibians has been studied and compared with Diplocaulus. A
moderately large sample of Trimerorhachis, comprising twenty-four
specimens, two specimens of Trematops, one of Batrachiderpeton
(from Watson, 1918) and one of Euryodus have been used. The
results, of course, are definitive for these genera only, but they
suggest that certain of the characters and certain methods may
have real value for more extended comparisons. It is possible to
demonstrate only that a particular specimen or suite of specimens
probably does not pertain to Diplocaulus, for lack of significant
differences does not show that single specimens or suites of speci-
mens are Diplocaulus. Furthermore, it is apparent, as would be
anticipated, that not all of the four features are definitive in any
one series of comparisons. Each case must be tested individually.
In the course of study of Diplocaulus it was found that two series
of values, derived by different methods, were useful in expressing
the nature of the relationships of the four linear measurements to
OLSON: DIPLOCAULUS 115
skull length, and in comparisons of the genus with other genera.
Certain features of the regressions of each measurement on skull
length, based on raw data, are of importance for comparison of the
nature and patterns of relative growth. Only Trimerorhachis, among
the Paleozoic amphibians, is represented by a sample adequate for
such comparisons. To increase the scope of this approach a sample
of Bufo marinus, studied by means of X-rays, has also been used
for comparison. Ratios of skull length to each of the measurements
in question have proven useful in more instances. These facilitate
generic comparisons in those cases in which other genera are repre-
sented by only a few specimens and in comparisons of individuals
with the sample of Diplocaulus. The regressions and ratios are, of
course, intimately related, but each has its own particular charac-
teristics and utility.
Three of the regressions, those of interorbital width, frontal
length, and parietal length on skull length, may be expressed by an
equation of the form Y=a+bX.! The pattern of relative growth is
essentially isogonic. The fourth, the regression of interparietal
length on skull length, is best expressed by an equation of the form
Y=bX*,? the growth pattern being heterogonic. Best fit has been
determined by comparison of the coefficients of correlation, r and p
respectively. This comparison cannot be made directly. The choice
1The symbolism throughout the paper has been adopted from Quantitative
Zoology, by Simpson and Roe (1939), in the belief that this book is more familiar
to the majority of North American vertebrate paleontologists than any other
standard work. Only in cases in which items not considered in that book are
treated in the present paper will the symbols used fail to appear in the appendix
of Quantitative Zoology (pp. 380-382).
2 As pointed out by Huxley (1932) and Simpson and Roe (1939) an equation
of the form Y=bX*k is commonly preferable when dealing with relative growth.
In many instances, however, the formula for isogonic growth gives equally good
approximations, and results obtained using one or the other equation do not
differ materially. The advantage of the form Y=a+bX, when there is little or no
choice of form, lies in the fact that it does not necessitate the use of logarithms and
is easier to manipulate. In the present paper I have used Y=a+bX where no choice
exists or where better results are obtained from such usage. It should be recognized
that use of this equation does not imply that there is no possibility that growth
was actually heterogonic.
In studies of the midline for reconstructions of skull outlines in section IV,
three of the relationships of bone lengths to skull lengths have been expressed by
equations of the form Y=a+bX while a fourth has been given as Y=bX*. The
heterogonic relationship is decidedly to be preferred for the last, but the others
are better or equally well represented by an isogonic expression. The heterogonic
equations for these three relationships, the regressions of Jow, Fri, and Pai on Ski,
treated as isogonic throughout the paper are:
j POPs telat Y=0.086X1-124
Was ee Y=0.980.X0-924
PQ Y =0.369X0-917
116 FIELDIANA: GEOLOGY, VOLUME 11
of function (in this case linear or log) depended upon which was
greater, r? or p”, since these values are estimates of how much of the
total variance is explained by the equation. The ratios in each
instance show a correlated regression on skull length but the value
of the constant 0 is low in all cases under consideration, and, since
the patterns of regression are not directly pertinent to growth, the
fact that they exist has been neglected in the comparative work.
The effect of the existence of regular change in ratios with change
in skull length is to increase the spread of the values of the ratios in
frequency distributions. They become somewhat less definitive than
would be the case were, for example, only adults compared. The
purpose of our work, however, is to make comparisons regardless
of size, so that the full array of values must be used.
Analyses of Diplocaulus
TABLE 12.—PARAMETERS OF ISOGONIC REGRESSIONS OF DIPLOCAULUS
N Mx My ox
Tow on Ski 34 86.5+14.8 13.5+2.3 33 .0+4.0
Fri on Ski 29 82.0+15.2 83.5+6.2 81.2+44.1
Paj on Ski 32 83.0+14.4 21.0+8.7 81.4+38.8
oY bxyY byx r
Tow on Ski 6.0+0.7 5.20+0.26 0.171+0.009 +0.95
Fron Ski 12.3+1.8 2.53+0.0097 0.392+0.0014 +0.99
Pajon Ski =7.8+0.9 3.83+0.175 0.248+0.011 UsoT.
RELATIONSHIPS OF INTERORBITAL WIDTH AND SKULL LENGTH:
The orbits of Diplocaulus are circular and closely spaced, being
directed dorsally or nearly so. Measurements of interorbital width
were made across the frontal normal to the midline of the skull at
the level of least interorbital distance. The regression of interorbital
width on skull length is treated as isogonic in character. The
estimating equation for this regression is Y=0.171X —2.49. Param-
eters for the regression are given in Table 12. Values of the ratios,
Table 13, in this instance as in all others, have been obtained by
dividing skull length by the values of the measurement in question,
in the present case skull length by interorbital width (Skj/Jow!).
In determination of the desired parameters, the mean (M) and
standard deviation (c),? the short method, as outlined by Simpson
1 For abbreviations of linear measurements throughout the paper see explana-
tions following Table 2.
2In cases of very small samples, those under N=25, o has been determined
by the formula o = Ni a i and is noted as o’.
OLSON: DIPLOCAULUS
117
TABLE 138.—RATIOS OF SKULL LENGTHS TO FOUR SERIES OF MEASUREMENTS
Ski
14
19
23
24
31
46
50
63
65
65
68
70
73
75
81
82
85
89
89
90
95
97
98
101
101
105
105
107
110
114
115
116
118
119
119
120
127
129
130
136
TABLE 14.— PARAMETERS OF FREQUENCY DISTRIBUTIONS OF RATIOS
Ski/Iow
Ski/Fri
Ski/Pa
Ski/Ipi
Ski/Iow
8.24
6.33
8.21
il
57
.33
.63
63
64
_~
or
N
34
29
32
31
IN DIPLOCAULUS
Ski/Fri
2.37
23
.67
.26
x4
.50
ra beg
£20
46
.59
59
40
.83
34
AE
31
387
.29
64
73
28
55
42
.59
44
=
IN DIPLOCAULUS
M
6.745+0.159
2.442 +0.036
8.914+0.077
4.442+0.087
Ski/Pa
3.
18
15
43
387
65
-76
20
06
78
-00
50
57
.95
31
47
24
Zo
.29
.80
78
384
48
38
82
35
80
42
24
10
-40
.07
.06
Ski/Ipi
for)
for)
o
0.927+0.112
0.197+0.026
0.4387+0.055
0.485+0.062
118 FIELDIANA: GEOLOGY, VOLUME 11
and Roe (1939), has been used. In determination of the parameters
of the frequency distribution of Ski/Iow, listed in Table 14, a class
interval of 0.5 was used.
RELATIONSHIPS OF FRONTAL LENGTH AND SKULL LENGTH: The
relative growth of these dimensions, so far as can be determined
from the sample, is isogonic. Pertinent parameters for the regres-
sion of frontal length on skull length are given in Table 12. The
estimating equation for the regression is Y=0.392X+1.0. Values
for the ratio of skull length to frontal length (Skj/Frj) are given in
Table 13. Parameters of the frequency distribution of the ratios,
determined using a class interval of 0.1, are listed in Table 14.
RELATIONSHIPS OF PARIETAL LENGTH AND SKULL LENGTH: The
relative growth of the parietal and skull lengths, as determined from
the sample, is isogonic. The estimating equation for the regression
is Y=0.248X+0.42. Parameters for the regression are listed in
Table 12. Values for the ratio of skull length to parietal length
(Ski/Paj) are given in Table 13 and the parameters of the frequency
distribution of the ratios, determined using a class interval of 0.2,
are given in Table 14.
RELATIONSHIPS OF INTERPARIETAL LENGTH AND SKULL LENGTH:
The pattern of relative growth of the interparietal with relationship
to skull length is expressed as heterogonic. The estimating equation
for the regression of interparietal length on skull length is
Y=0.117X1-155, Parameters of the regression are as follows:
N log MX log MY k b
30 1.86256 1.21933 1.155 0.117
Values of the ratios of skull length to interparietal length (Skj/Ip1)
are given in Table 13 and the parameters of the frequency distribu-
tion of the ratios, determined using a class interval of 0.3, are listed
in Table 14.
The data listed in Tables 12-14 are analogous to verbal descrip-
tions of skull characters and may be used in a somewhat similar but
more precise fashion. They have an advantage of simplicity and
may be used to express relationships of characters at desired growth
stages. Their principal advantage, however, is that they are subject
to rigid, objective treatment. The limitations of the data are those
inherent in small samples. It is probable that, while use of larger
samples would modify the values somewhat, addition of more
specimens would not alter the results materially. Modifications of
OLSON: DIPLOCAULUS 119
the concept of the genus so far as the characters studied are con-
cerned would be analogous to refinements introduced into verbal
analyses by study of additional specimens. In the following para-
graphs, the utility of the data will be tested in comparison of genera.
Comparison of Genera
The comparison of genera may be approached in various ways
and at several levels. Generic assignments may be, and usually are,
based upon characters that, in the opinion of the observer, are
significant in the case or cases with which he is dealing. This was
the method used in assembling the samples of Diplocaulus and
Trimerorhachis for the present study. It is a necessary preliminary
to the types of analyses carried out in the present section. Once
the samples have been assembled, various comparisons may be
carried out depending upon the objectives of the work and the nature
of the comparative material available. The remaining part of section
III is devoted to such comparisons.
The various specimens and samples that are here compared with
Diplocaulus consist of carefully identified materials. At the outset
we know that they are generically different from Diplocaulus. It
has been pointed out that four relationships in the skull of Diplo-
caulus are moderately constant within the genus. Our object is
to test these relationships in various ways in order to study their
utility in differentiation of other genera from Diplocaulus and to
determine, as far as possible, if the relationships are characteristic
of Diplocaulus. To this end, three types of analyses have been
made: (1) comparison of regression lines based on raw data; (2) com-
parison of sample means based on ratios; and (3) comparison of
single specimens with the sample of Diplocaulus based on ratios.
(1) COMPARISON OF REGRESSION LINES: Regressions expressing
relative growth appear to follow a pattern of heterogony in most
eases, as brought out by Huxley (1932). In two of the four regres-
sions to be considered in this work (Jow on Skj and Paj on Skj), the
it of the regression line to the data by the formula Y=a+bX is
yetter than that obtained by using the formula Y=bX*. In the case
of Frj on Skj an equally good fit is accomplished by both formulas.
_n these three instances the form Y=a+bX has been used. Equa-
tions of the form Y=bX* for each of the regressions have been given
i1 the footnote on page 115. Since only equations of these two forms
< re pertinent in the present studies, the number of types of differences
t etween regression lines is limited. The most obvious difference is,
120 FIELDIANA: GEOLOGY, VOLUME 11
of course, that between the two types of formulas. Where it has
been found that a certain relationship in one genus has one form
and that the same relationship in another genus has the other, a
real difference has been demonstrated. Where two or more samples
show the form Y=a-+bX either a or b may differ or both may differ.
Appropriate tests are available to determine the significance of such
differences. Significant difference in 6 (byx in the regressions as
used in this paper) denotes differences in the slopes of the lines. In
instances in which significant differences in slope cannot be demon-
strated, differences a (ayx as used in this paper) may be important.
In those cases where regression lines are parallel, differences of a
indicate, in addition to lack of conformity of the point of intercept,
lack of coincidence of the two lines. The approach to these problems
involves testing the hypothesis that the two or more samples could
have been drawn from the same population. In the case of Y=bX*,
analogous differences may be tested, k being an expression of slope
on a logarithmic plot and } an expression of position. This is clear
by comparison of Y=a+bX and the logarithmic form of Y=bX*,
which is log Y=log b+k log X.
TABLE 15.—MEASUREMENTS OF TRIMERORHACHIS
Specimen
number Ski Tow Fri Pai Ipi
BiM 4669) esc sc: 37.6 11.6 7.0 16.2 bets
ROM ETLIG 4 fae oon 54.4 13.0 ee 3
NE LEA Ge eee. 58.5 8.3 ge re
yd. Dae 2 Ds pa rea ay ea 62.3 10.0 18.5 21.5
7 NG Hee fi 0 eae ane oe 65.4 10.3 19.3 ras ta |
] We VR gh ERM Oe eet 67.9 10.5 20.0 26.0
POMS CULO oe: o3 onic cc 70.6 cy cote i ee.
TM 1600 see ees 78.7 Tae 22.0 23.5 10.0
|G 6G Le Serene ae 80.0 14.0 kc ane fey
A.M. 7116.. 80.7 13.9 23.2 Sie
AMS TAIG. oo aed « | 13.2 ane eee idee
iM 16009 213. 5.53: 81.5 16.6 eas ae 10.8
A.M. 7116.. 87.5 16.1 26.5 30.5 bras
AMS 15906 ee 89.0 17.3 aa: Aa: ap
yl an a 8 0 ee ee 102.4 18.1 we 39.4 ee
UM AG009 5 i sestax 106.0 15.2 27.0 28.1 10.0 >
UM 1G008 3 ie cor 107.1 18.6 36.7 34.8 11.5
US Oe: ) erent ae 109.0 20.0 38.0 31.0 13.0
RC) GOS 6. ene 115.0 21.0 38.5 39.0 13.0
RC. UCR. cess a: 118.0 20.0 41.0 34.0 12.5
BM OADTOS os eke 122.5 23.5 es 31.3 reat
MC: 1008io5 sc: 131.0 23.4 46.0 36.3 12.3
ANE -4560 4... sos 141.0 21.8 41.0 46.6 Rese
AMS 4692) tits ca 172.6 31.5 rite Bere
Our efforts in such tests are drastically limited by available
materials. Among Paleozoic amphibians, only Trimerorhachis has
U
OLSON: DIPLOCAULUS 121
been available in sufficient numbers to allow comparisons of regres-
sion lines. Data for the sample of this genus are given in Table 15.
Bufo marinus has been studied from a sample comprising 112
individuals. Results of these tests are not included, since they are
not germane to the problem, but it should be noted that in all
instances highly significant differences occurred. The tests involving
Diplocaulus and Trimerorhachis fall into two categories, tests of
differences of slope and tests of differences of position of the regression
lines. The former includes analyses of relationships expressed by
both the equations Y=a+bX and Y=bX*. These tests involve the
general concepts of analysis of variance but, in the tests of slope,
we have used the equation of Simpson and Roe (1939, p. 278) and
an equation modified from it to be suitable for the use of logarithms.
Tests for position have been based on analysis of variance, following
the procedure of Tippett (1945).
Tests of Slope: The equation used for these tests so far as regres-
sions conforming to Y=a+bX has been taken from Simpson and
Roe, but modified so that t, for evaluation of significance of differ-
ence, is attained directly from the equation by using byy, (regression
coefficient for Diplocaulus) minus byx, (regression coefficient for
Trimerorhachis) as the numerator and the Simpson and Roe equation
as the denominator. The equation thus becomes as follows:
b, — bz
~ [s(@) 1-4) + 3) G7) 1 1
V None 4 (san a7 sun)
Entering a table of ¢, as in Simpson and Roe (1939, p. 206) or
Snedecor (1946, p. 65), the significance of difference may be deter-
mined. Results for the three regressions tested, interorbital width,
rontal length and parietal length on skull length are given in
Table 17. N and r for the regressions are given in Table 16.
TABLE 16.—VALUES OF N AND r FOR DIPLOCAULUS AND TRIMERORHACHIS
1X plocaulus Tow Fri Pa
Est. Equation Y=0.171X—2.49 Y=0.329X+1.00 Y=0.248X+0.42
Ni 34 29 82
r +0.970 +0.992 +0.974
1 rimerorhachis
Est. Equation Y=0.16X+1.48 Y=0.387X—5.52 Y=0.241X+7.7
N. 24 14 16
2
T2 +0.906 +0.995 +0.875
122 FIELDIANA: GEOLOGY, VOLUME 11
TABLE 17.—RESULTS OF TESTS OF SIGNIFICANCE OF DIFFERENCES
oF bY X; AND bY X2 IN DIPLOCAULUS and TRIMERORHACHIS
Item a.f.* t J aha
Tow 54 0.58 0.5
Fri 39 1.52 0.1
Pa 46 0.61 0.5
*d.f.=degrees of freedom; P=probability.
It is evident that in none of these three tests does the probability
approach a value that allows the interpretation that the difference
is significant. Throughout much of the paper a limit of 30 has
been used (P=0.008) but in comparisons of regression we will use
P=0.01, the lowest value for P given in most tables, as the critical
level. The results show that the slopes of the three regression lines
under consideration cannot be thought characteristic of the genus
Diplocaulus, since they are not significantly different from those in
Trimerorhachis.
The relative growth of interparietal length and skull length, as
expressed in the regression of interparietal length (Y) on skull
length (X) in both Diplocaulus and Trimerorhachis, is heterogonic
and may be expressed by an equation of the form Y=bX*. In
order to deal with a rectilinear regression line for comparison the
figures must be treated logarithmically. An equation, equivalent
to that on page 121, has been used for this purpose:
k, —k,
dl 1 12 log Xed log Y2)?
ae log Y,) — 2@log Xidlog Yio! + x(drlog Y,) — “oer aloe. _)
N, - N, aan 4
1
x
1 ef al
| log X1) ' =(d? va)
N, is 29 and Ne is 8 (Diplocaulus and Trimerorhachis respectively)
and the estimating equations giving the value of k are Y=0.117X1-155
for Diplocaulus and Y=1.503X9-439 for Trimerorhachis. Using the
equation the results in Table 18 are obtained.
TABLE 18.—RESULTS OF COMPARISON OF k (Ipi ON Ski)
IN DIPLOCAULUS AND TRIMERORHACHIS
d.f. t P
Ipi 33 11.5 <0.01
OLSON: DIPLOCAULUS 123
At the 0.01 level of significance for 30 degrees of freedom, t= 2.750.
Thus it may be concluded that in this test Trimerorhachis and Dip-
locaulus are significantly different.
Tests of Coincidence of Lines: For comparable lines in the two
genera in which slope does not differ significantly, it is of interest to
test the coincidence of lines. This may be approached by the method
given by Tippett (1945), an application of analysis of variance to
position of regression lines. This proceeds on the hypothesis that
two or more samples were drawn from a single population. The
samples are combined to form a single sample and are also treated
individually. Comparison is then made between the independent
(between arrays) and residual (within arrays) sources of variance.!
Results obtained by this method are given in Table 19.
TABLE 19.—RESULTS OF ANALYSIS OF
VARIANCE TESTING COINCIDENCE OF REGRESSION LINES OF Iow,
Fri, Pat ON Ski IN DIPLOCAULUS AND TRIMERORHACHIS
Ni* N2* ad: F F for P=0.01
Tow 34 24 { With wooo oe \ 14.1 5.01*
Fri 29 12 { Wikh aan be \ 103-0 5.21*
Pa 32 16 { Wether nee! ta \ 32.8 5.12
*N, applies to Diplocaulus and N2 to Trimerorhachis. For Iow based on degrees
of ee between arrays=55; for Fri based on degrees of freedom between
arrays=88.
1 Since I have found no instances of use of this method in paleontological
literature, a few words of explanation may be in order. The sum of the squares
of the residual source of variance are determined for the two samples—more may
be used—by the equation:
. _ (edXid¥,)? (2axsa¥.))
Pa (:ey: oe ) oie (ze, _ oe
where Y; and X: represent Sample 1 (Diplocaulus), and Y2 and X: represent Sample
2 (Trimerorhachis). The sum of the squares for variance within arrays is obtained
from the expression:
(zey: = ee) ae
ra?X!
vhere =d?Y! is the sum of the squares of the deviations of Y from the grand mean,
»d?X! is the sum of the squares of the deviations of X from the grand mean, and
2dX'dY! is the sum of (deviations of Y from the grand mean) X (deviations of X
‘rom the grand mean). To obtain variance in each category the sums of the
:quares for the independent and residual sources of variance are divided by
_ the degrees of freedom for each. The independent variance is then divided by the
1esidual and the significance of the difference may be obtained from a table of
." (variance ratio) as given on pages 222-225 of Snedecor (1946). This method is
{illy explained by Tippett. The symbols that he used have been converted to
t rose followed in the present paper.
124 FIELDIANA: GEOLOGY, VOLUME 11
There is a high degree of significance in each of the F values
and the hypothesis that the pairs of samples came from the same
population is negated. We have found then that, although the
pattern of relative growth between the length of the three bones
considered and skull length is the same within observed limits of
skull lengths, that there is a ratio difference in the relationships
considered, that is, the relationship of the linear measurements of
the three bones to skull length. This difference is reflected in studies
of ratios in a later part of this section. In this aspect of the regression
lines there is a real difference between the two genera.
If the various lines be extrapolated to X=0 it becomes apparent
that a biologically impossible situation occurs. In cases in which
Y is negative, a real situation may be expressed when Y=0, for the
skull may have length prior to the appearance of dermal bones.
Dermal bones do not commonly appear in a single, small area and
grow by simple accretion or expansion but rather as osteoblasts
over a wider area, so that even in a very early stage of development,
at the time of first appearance of a bone as an entity, which must
be somewhat arbitrarily defined, the bone has a finite and not in-
considerable length as compared with skull length. We cannot say
how far back in ontogeny there originated the pattern of relative
growth that we have determined for Diplocaulus and Trimerorhachis.
It seems evident, however, that there were drastic changes in the
nature of most of the curves in early stages of development. Since
this is certainly true for those in which the value of Y is positive,
it is almost certainly the case as well in instances where the value of
Y is negative, although this is not clearly demonstrated. The
pattern in Diplocaulus appears to have been established by the
14 mm. stage. If we extrapolate the line, for example, of the regres-
sion of parietal length on skull length so that X=0, then Y=0.42,
an impossible situation. Therefore, between X=0 and X=14,
changes not evident in the line of regression must have occurred.
Huxley (1932) pointed out that in early embryonic periods, during
histological differentiation, growth rates are different from those
such as we have determined. In this stage occurred the develop-
ment of the bones that we are studying. In Diplocaulus, since we
know the pattern at a very small size, we may surmise that the
stage of establishment of the pattern of relative growth that we
have determined, followed very closely upon the stage of differentia-
tion of the dermal bones. The evidence in Trimerorhachis is less
conclusive.
OLSON: DIPLOCAULUS 125
A study of Bufo marinus has been made to accompany that of
Diplocaulus, as noted above. It is apparent in this genus that the
pattern in various relationships of skull bones, either isogonic or
heterogonic as the case may be, is established at the time, in the
metamorphosed individuals, when the limits of the bones can be dis-
tinguished in the X-rays. In cases where the bones have not as
yet met, if one-half of the distance between bones is added to each,
the relationships of the bones to skull length is that which would
be predicted by extrapolation of the curve based on larger and
more mature individuals. It thus appears that in this species the
pattern of relative growth originated at a very early stage, prior
to the complete roofing of the skull.
We may assume, on fairly sound evidence, that this was the case
in Diplocaulus and, on less good evidence, that it was true for
Trimerorhachis as well. If this is so, the lack of coincidence of
regression lines, even though the slope is about the same, has real
meaning for any stage that might be expected to occur in the fossil
record. How generally the regressions of Diplocaulus would differ
from those of other Paleozoic amphibians cannot be stated, because
of the lack of adequate samples. Regression lines may be charac-
teristic of the genus, but it would require analyses of samples of
all amphibians now known plus all those which may be found to
even approach a reasonable answer.
(2) COMPARISON OF MEANS: Of the Paleozoic amphibians avail-
able for comparative studies, only Trimerorhachis is represented by
a sufficiently large number of specimens to allow a profitable com-
parison of means of samples. The procedure involves comparison
of the means of the frequency distributions of the ratios.. We
know that the two samples represent different genera. The problem,
then, is whether the variates to be tested for the two samples differ
significantly in their means. To make the comparisons the following
formula has been used:
oi, oO
oq = + ———
Ni Ne
In, no case does Ni+Ne equal less than 30. For these tests, however,
o’ has been used for o in the equation. In each instance, here as in
the following pages, the subscript ; refers to Diplocaulus and the
subscript 2 to Trimerorhachis.
1 The accurate use of frequency distributions of ratios for comparisons involves
the assumption that Y=a+6X expresses the relationships of the pairs of values
and that the value of a is 0 or close to 0. To the extent that the data fail to con-
form to these conditions, inaccuracies are introduced.
126
FIELDIANA: GEOLOGY, VOLUME 11
TABLE 20.—RATIOS OF SKULL LENGTHS TO FoUR MEASUREMENTS
Ski
37.
141.
172.
DOONOSOHOROAMMHASIBDORWOARA
DID D CVO OT ON OID CLOT OTE AD |D OIA AAA HD A CO
HR O10T WW CH O11 00 OTR OOF HOO RO OWN DN >
Ski/Iow
IN TRIMERORHACHIS
Ski/Fri Ski/Pai Ski/Ipi
Sag Dea Shere
3.87 2.90
3.16 Zale
3.28 2.61
3.58 3.35 7.87
3.48 2.59 Siu
ay cee 7.54
3.30 2.87 eee
of 2.60 10.60
3.93 STE 9.30
2.85 3.07 Boe
Vago 3.52 8.38
2.99 2.95 By eS
2.88 3.47 9.44
oe oe 3.91 ee
2.85 3.61 10.65
a ee 3.03 eer
3.44 cee
TABLE 21.—PARAMETERS OF FREQUENCY DISTRIBUTIONS OF RATIOS
IN DIPLOCAULUS AND TRIMERORHACHIS
N
Ski/Iow 32
Ski/Fri 30
Ski Pal. oe
Ski/Ip 31
Diplocaulus
M
6.745+0.17
2.442+0.04
3.914+0.08
4.442+0.11
o’ N
0.945+0.12 23
0.194+0.03 13
0.446+0.06 16
0.494+0.06 8
Trimerorhachis
M
5.859 +0.18
3.210+0.09
3.080+0.08
8.983 +0.32
o’
0.810+0.12
0.3872+0.07
0.442+0.08
1.090+0.27
Comparison of Diplocaulus and Trimerorhachis: Ratios for
Trimerorhachis are given in Table 20 and the parameters for the
frequency distributions in the two genera in Table 21. Results of
calculations determined for d/cg, with oq determined from the equa-
tion cited in the preceding paragraph, are summarized in Table 22.
It is evident that the means of the two samples are significantly
different for each of the comparable frequency distributions. Samples
of Diplocaulus and Trimerorhachis can be separated by use of the
means of the ratios of the skull length to the four linear measurements.
TABLE 22.—RESULTS OF COMPARISONS OF MEANS
IN DIPLOCAULUS AND TRIMERORHACHIS
d/o'd
Ski/Iow Sit
Ski/Fri —7.1
Ski/Pat 6:1
Ski/Ip —11.5
OLSON: DIPLOCAULUS 127
Materials to extend such tests to other Paleozoic genera are not
available. It would be desirable to conduct such tests on all known
genera of Late Paleozoic amphibians, for only by such a complete
series of tests could it be determined whether or not the ratios of
Diplocaulus are probably characteristic of the genus. Tests involv-
ing comparison of means, as used in such cases, can, of course, be
made only on samples of known composition. Their function is
not to differentiate samples, although such use may be made of
means by slightly different methods, but to test the differences in
one or more features between groups known to be different on other
bases.
It must be emphasized that a significant difference in the means
does not imply that all or even a large percentage of the specimens
in one sample would show a significant difference from the other
sample in the character tested. This is made clear in the next series
of tests, which involve comparison of single specimens of Trimer-
orhachis with the sample of Diplocaulus. It is possible, however,
in any large sample, to calculate the percentage of specimens that
probably would be significantly different.
(3) COMPARISON OF SINGLE SPECIMENS WITH DIPLOCAULUS:
Determination of the probability that a single specimen could have
been drawn from a “population” from which a sample was derived,
in this instance the sample of Diplocaulus, is by far the most useful
of the methods discussed in this section in view of the difficulty of
obtaining adequate samples of most genera. The procedure involves
determining the absolute distance (expressed by d) of the appropriate
value for the specimen being tested from the mean of the sample
with which comparison is being made, and division of this value by
the standard deviation of the sample (c). The probability that it
could have been drawn from the population is readily determined
from the value of d/c. As before, we will use 30 as the critical level
of significance.
The simplest approach to this problem is to determine 30 for
each of the desired frequency distributions of the sample and the
value of d for the appropriate characters of each specimen. Whether
or not the difference is significant can then be determined by in-
spection. Since, however, 3c has been arbitrarily selected, more
precise figures from which probabilities may be determined have
been obtained in the present work from d/c.
In each of the cases tested, the approach is designed to test the
utility of the ratios when used in the manner outlined, for, of course,
128 FIELDIANA: GEOLOGY, VOLUME 11
it is already known that the specimens are not Diplocaulus. As
in earlier tests, the results are definitive only for the genera tested
and few generalizations can be made.
Trimerorhachis and Diplocaulus: In each of the four series of
ratios all specimens of Trimerorhachis that have yielded a particular
measurement are tested against the sample of Diplocaulus by the
method outlined above. The results of the tests are shown below
in Table 23. For rapid estimation the values of 3c are also entered.
For M and o of Diplocaulus see Table 14.
TABLE 23.—COMPARISONS OF SINGLE SPECIMENS OF TRIMERORHACHIS
WITH THE SAMPLE OF DIPLOCAULUS
Values of 30 for Diplocaulus
Skt/l0g koh 2.181
Ski Prise 5202592
SIP ONG} eg ccs 1.411
el 48 67 Ree aie We 1.454
Ski/Iow Ski/Fri Ski/Pai Ski/Ipi
Ski d d/o /o d d/o o
87.6 3.825 SiGe asa 1.63 Sub take.
54.4 2.545 PANS cig Men ee LTT Le mee MEMES oa Rl cau Tee een
58.5 0.3850 Ort ee Ce eee ALL I eg me
62.38 0.545 0.7 —0.93 —4.8 1.01 5S: Male OA:
65.4 0.3805 0.3 —0.72 —3.7 1-25 208 Mela
67.9 0.254 0.3 —0.84 —5.3 1.30 7 Slee ae ae
70.6 0.745 Ute ie a ae ee es ee ee Re
78.7 0.345 0.4 —1.13 —5.7 0.56 1.8 —3.43 —7.1
80.0 0.945 1; Emenee wee ee Pr NS RAs
80.7 0.645 O27 —1.04 —5.3 1.42 Sisee a ae has
81.1 0.645 QIN Ae ae ks SNe ciel nine cesta el Bear, Wer th oases
81.5 1.845 | Ae Rar Nee on —3.10 —6.4
8725 1.245 1.3 —0.86 —4.4 1.04 Diehl Aer ste os
89.0 1.645 1 Oy. eae Oo Pe nes ene nb Ny
102.4 1.045 Petter whe ey = 1:81 3.0 —6.16 -—12.9
106.0 0.155 0.2 —1.48 —7.5 0.24 0.6 —4.86 -—10.1
100-1" 20.946 Dez —0.41 —2.1 0.84 i9 —3.94 —8.1
109.0 1.245 1.8 —0.33 —1.7 0.39 Re tate Rk
115.0 1.245 Is —0.55 —2.8 0.96 7 Sy A Pe Pag he Ae
118.0 0.845 0.9 —0.44 —2.3 0.44 TO —5.0 —10.3
122.5 1.445 dA Ree reo mK 0.00 OR OL EwE ete: fee
181.0 1.146 132 —0.41 —2.1 0.30 0.7 —6.2 —12.2
141.0 0.245 ONS | Teas Sed 0.87 i at! EA one eee Bare
LiZ26: etl.345 1.4 —1.00 —5.1 ero Seen Stee Parr re
Table 23 shows that the probability of differentiating a specimen
of Trimerorhachis from the sample of Diplocaulus by this method is
low, for Ski/Iow and Skj/Paj. The ratio Skj/Frj accomplishes a
separation in eight of thirteen cases tested. In only one case is
d/o<2. The values of d/o in the case of Skj/Ipi are so high that
differentiation probably will occur in all cases that may be en-
countered.
OLSON: DIPLOCAULUS 129
Trematops and Diplocaulus: Although these genera are only
distantly related they have certain resemblances, particularly in
midline characters, that could prove confusing in small specimens.
The following tests serve to illustrate ready means of differentiation.
Linear measurements, ratios and results of tests of significance are
given in Table 24.
TABLE 24.—LINEAR MEASUREMENTS AND RATIOS OF TREMATOPS,
AND SIGNIFICANCE OF DIFFERENCES FROM DIPLOCAULUS
Linear Measurements
Specimen
number Ski Tow Fri Pa Ipi
M.C. 1584 70 Ly 19 15 (ie
M.C.Z. 1414 74 16 23 17 8.5
A.M. 4205 145 30 - - aod
Ratios
Ski Ski/Iow Ski/Fri Ski/Pai Ski/Ipi
70 a) 3.7 Uae Sor
74 4.6 3.2 4.3 9.3
145 4.8 Mee oe eee
Significance of Differences
Ski Ski/Iow Ski/Fri Ski/Pa Ski/Ipi
d d/a d d/o d /o d o
70 2.645 2.8 —1.258 -6.4 -—0.786 -1.8 -—4.858 —10.0
i4:~ -2 146 2.3 —0.758 -—8.8 -—0.886 -—-0.9 —4.258 —9.2
145 1.945 raat |
Neither the ratio Skj/Iow nor Skj/Paj shows significant differences
from the mean of the sample upon the basis of 3c, but the values
of Skij/Iow do show probabilities of less than 0.04 in all cases and
of 0.005 in the case of U.C. 1584. Both examples of the other two
ratios show significant differences from the sample of Dzplocaulus.
The results in general agree with those obtained in comparisons of
single specimens of T'rimerorhachis with the sample of Diplocaulus.
Batrachiderpeton and Diplocaulus: The data on Batrachiderpeton,
Table 25, have been taken from the illustrations given by Watson
(1913). This genus is of particular interest in view of the fact that
it is a Pennsylvanian relative of Diplocaulus. If it be assumed that
it is near to the ancestral line of Diplocawlus—and there is some
evidence to support such a conclusion—the comparisons give insight
into certain changes that have occurred in the evolution of Dzplo-
caulus. A single specimen is hardly adequate for reliable conclusions
but the comparisons, at least, give some insight on the general
direction if not the magnitude of changes. Tabulations for com-
parative purposes are included in Table 25.
130 FIELDIANA: GEOLOGY, VOLUME 11
TABLE 25.—LINEAR MEASUREMENTS AND RATIOS OF BATRACHIDERPETON,
AND SIGNIFICANCE OF DIFFERENCES FROM DIPLOCAULUS
Linear Measurements
Ski Tow Fri Pai Ipi
7 88 15 9 14 7
Ratios
Ski/Iow Ski/Fri Ski/Pai Ski/Ipi
2.35 4222 2.07 5.43
Significance of Differences
Ski/Iow Ski/Fri Ski/Pa Ski/Ipi
d o d d/o d d/o d o
4.215 4.4 —1.778 —9.0 0.844 Lg 0.988 2.0
If we may consider the differences of the single specimen of
Batrachiderpeton from the sample of Diplocaulus as a general indica-
tion of generic differences between the two, certain interesting points
may be made. The ratio of Ski/Iow of Batrachiderpeton is signifi-
cantly different from that of Diplocaulus. In Watson’s discussion
(1913) of bone homologies of the orbital region, he stressed the
effect of lessening interorbital width in the morphological changes
by which Batrachiderpeton might approach the condition of Dzplo-
caulus. This, being written when relatively few specimens of
Diplocaulus were known, particularly in the smaller sizes, might be
open to question on the basis that comparison did not take into
consideration the pattern of growth in Diplocaulus. But here we
see that the difference is significant even when a large sample in-
cluding a wide range of sizes is considered. Inasmuch as there is
actually a negative regression of the ratios on skull length, it becomes
apparent that the condition compared is more pronounced when
specimens of Diplocaulus of about the same skull length as Batra-
chiderpeton are considered than when the latter is compared with
large specimens of the former. Furthermore, it may be noted that
the differences in the ratios is in contrast to the lack of significant
differences in the comparison of the labyrinthodonts Trimerorhachis
and Trematops with Diplocaulus. In all genera tested to this point,
the ratio of Skj/Paj is similar. The ratio Ski/Fri of Batrachiderpeton
is decidedly different from that of Diplocaulus, so different that it
appears improbable that any of the values that might be obtained
from a sample of Batrachiderpeton would fail to show significance.
It is difficult, and probably incorrect, to apply to this case the
methods of Simpson and Roe (1939) for determining the probable
variability of a taxonomic unit represented by a single specimen,
OLSON: DIPLOCAULUS 131
since the method involves the coefficient of variability (V), which
has questionable applicability in a group without definable terminal
growth (see discussion, pp. 144-149). The ratio of Skj/Ipj is not
clearly significantly different in Batrachiderpeton and the sample of
Diplocaulus (d/c=2.0). This is in striking contrast to the situation
with respect to Trimerorhachis and Trematops, in which the difference
shows a high level of significance.
Euryodus and Dviplocaulus: Euryodus is a gymnarthrid and
probably more closely related to Diplocaulus than Trimerorhachis
or Trematops. The skulls of gymnarthrids are subject to confusion
with small skulls of Diplocaulus unless certain critical structures are
visible. If it is possible to show that there is a good chance of
differentiation, using midline characters, which are commonly
preserved, difficulties of differentiation will have been much reduced.
Linear values, ratios, and the significance of comparisons with
Diplocaulus are given in Table 26.
TABLE 26.—LINEAR MEASUREMENTS AND RATIOS OF EURYODUS
AND SIGNIFICANCE OF DIFFERENCES FROM DIPLOCAULUS
Linear Measurements
Ski Tow Fri Pai Ip
32 10.0 ise 11.8 5.5
Ratios
Ski/Iow Ski/Fri Ski/Pai Ski/Ipi
8.2 4.4 pe f 5.8
Significance of Differences
Ski/Iow Ski/Fri Ski/Pai Ski/Ipi
d o d/o d d/o d d/a
3.545 3.8 —1.958 —9.9 de214 2E8 1.358 2.8
As in the case of Batrachiderpeton, Ski/Iow and Skj/Frj differ
significantly in Euryodus from the sample of Diplocaulus. The
values of d/o in these two sets of comparisons are quite comparable.
Likewise Skj/Paj and Skj/Ipj are not certainly significant, although
both, in which d/c=2.8, are very near the selected level of 3c.
The two lepospondyls tested against Diplocaulus show a common
pattern of differences and the two labyrinthodonts another common
pattern. That this is more than coincidental for the two groups
cannot be demonstrated from the limited materials available for
study. There is, however, a suggestion here of an area for additional
study, for should some such pattern emerge from more extensive
132 FIELDIANA: GEOLOGY, VOLUME 11
investigation, the sample of Diplocaulus might prove of considerable
value in determining the major affinities of specimens that are
difficult to place.
IV. GROWTH AND VARIATION
METHODS
The data thus far presented have indicated that the most profit-
able approach to studies of problems of growth and variation in the
skulls of Diplocaulus would be through analysis of changes of total
shape. This could be supplemented by more detailed analyses of
changes of individual bones but, for the present, studies have been
limited to the broader problems of shape change.
The problems of changes of shape with changes in size are complex
and special methods must be applied to various cases. It was found
in the present studies that none of the more conventional methods
was satisfactory. Deformed co-ordinates, for example, give a
moderately satisfactory visual concept of changes but do not permit
a comprehensive quantitative analysis, and various graphical and
_ numerical methods were abandoned in favor of the ones discussed
below, either because they did not give an adequate concept of change
or because they could not be applied because of incompleteness of
materials.
The change of shape with size, as used, is based upon change in
size as expressed by increase in length of midline length of the skulls.
Certain general conclusions may be reached by inspection of the
specimens of the sample. Maximum width increases disproportion-
ately with respect to skull length. There appear to be marked
differences in skull width in skulls that do not differ markedly in
length. These differences are sufficient to lead the observer to
expect only moderate correlation between increase in skull length
and increase in width. There is, further, a suggestion that increase
in width will show a positive heterogonic relationship to increase
in length.
To test the validity of these observations it has been necessary
to apply quantitative methods. Since the skull as a whole is subject
to changes in size, there is no point that can be considered as stable
within the area defined by the outline of the skull. It would be
possible, of course, to select any point that could be determined on
all specimens, and use it as a basis for measurements, arbitrarily
133
134 FIELDIANA: GEOLOGY, VOLUME 11
assuming it to be fixed, but this could give no more than an ap-
proximation of true conditions. It has been found more practical
and realistic to recognize total plasticity and base measurements
on a series of points whose relationships to change in midline skull
length, the base measurement, may be understood. Since we are
dealing with changes of shape of the whole skull, and not of com-
ponent bones and bone limits or junctions, or positions defined by
other skull features, points may be used only if their relationships
to the basic change in size are relatively simple. None of the de-
finable points along the skull margin, except the anterior and
posterior termination of the midline, bear simple relationships to
change in skull length. Points defined by sutural junctions, such
as that of the parietal, supratemporal, and squamosal, do not show
uniform and simple changes as the skull length increases. It has
been shown, however, that a series of points along the midline—
(1) the level of the anterior orbital margin, (2) the junction of the
parietal and frontal, and (8) the junction of the parietal and inter-
parietal—do show a relatively simple and regular relationship to
change in skull length in D. magnicornis. These points, plus the
posterior termination of the midline and the horn tips, may be used
as base points at which significant measurements of skull width
may be made. The point of intersection of a line through these
points, normal to the midline, and the skull margin is significant
since it relates a point on the skull margin to a point that shows
regular change in skull length.
Points of intersection, so derived, migrate laterally as skull
length increases and the length of the lines between the points
defined on the left and right sides of the skull may be taken as a
measurement of skull width at homologous levels along the midline.
Using the five levels specified in the preceding paragraph, we may
derive the following measurements of width:
W.=Width at anterior margins of orbits.
W:2= Width at junction of frontal and parietal.
W3= Width at junction of parietal and interparietal.
W.= Width at posterior termination of midline of skull.
W;= Width at posterior termination of horns.
Measurements of skull length pose difficulties much like those
encountered in width measurement, for homologous points along
the posterior margin of the skull cannot be used because of the
difficulty of determining their location and because of their variability
in position. Length measurements should show some dependency
TABLE 27.— MEASUREMENTS OF SKULL WIDTH (W) IN DIPLOCAULUS
Specimen number Wi
A.M.N HUAGZ8A oreo. 7
UC 20G +4 oe ens 13
A.M.N.H. 4523B....... 12
A.M .N.A, 4752). 8.4: 20
WG oO AG eae teas tries 40
AUMAN 4485 3s 27
7 08. a ss I || ee 45
WG Cees 2: vad Coes 45
UO 2 1668 occ ieee. 52
UC 1668 5 Hie ie os 47
Dn cg -+: A a 51
AMUN A 4611 senses
Re AIO hte oes 60
PUZOSO eae ee ae 56
BES DBO ee rcs et 62
ACME ADI2: cio. on 66
WC 1OB ser seas 7
A.M.N.H. 4504........ 80
We Bal tae ta sce
A.M.N.H. 4469........ 74
WC CALOLG oe snare at
A.MIN.B: 44940. oe 75
ACM NE. 46165 Gk 78
WG 064s hea eek 98
ALMUN 4408 0 8. a 85
A-MLN.H. 44665 033: 100
ADMIN A467 ocd as 80
Ms GO sc iis anges eras
AMON. 44722. 22%: 103
AMEN 2001 ok, 112
Specimen number Ty
A.M.N.H. 4523A 15
WG 1660 os hee ee
| 9 O52), UA ens re Ve 23
A.M.N.H. 4523B....... 21
A: MEN. A162 oe ae 26
AM ON A490 es tee 52
ASM. NA ASS6 o 12
WO ae ric cst. oaleacsteee 70
WG 1 Oe hi eg eae 70
COR TBBS hice ert cei
| OF y+’. Raa ee cae ete 72
WUC AOS i tenant 83
POD ian evecare wig 93
WC LOGO xa sto se ee 98
ARENA 46128 Oo aia 99
UC lO encores claw:
A.M.N.H. 4504....... 103
Menace one ae 105
A.M.N.H. 4469....... 104
UC. 1016 22: SM sors 102
A.M.N.H. 4478.23... 115
AM NH 4614) eu) 118
Co 664 tk cee, 114
AMEN. 4498 23360. 116
4.M.N.H. 4466....... 120
AMON.H: 4467 56350 119
DAoe OBO Lard stage seve 120
AIM UN 447 2s 131
W2
Ws
136 FIELDIANA: GEOLOGY, VOLUME 11
upon variations that appear in the width measurements. Series of
points determined on equally spaced lines, as used for example in
Test 14 (pp. 99-100), fail in this respect, since they do not take into
consideration the changes in relative rates of width change with
increase in skull length. “The points along the posterior margin
likewise should bear relationship to changes in midline skull length.
To accomplish these two aims it was necessary to depend primarily
upon the points established for width measurements along the lateral
margins of the skulls. Through each of the points determined for
width measurements lines parallel to the midline were drawn to
intersect the posterior margin of the skull and to a line constructed
normal to the midline at the level of the tip of the snout. The
lengths of the various lines so constructed were designated as L.
In addition, a more medial measurement was derived by constructing
a line parallel to the midline of the skull through the center of the
orbit. It can be shown that the distance from the midline to the
level of this line changes in essentially isogonic relationship to skull
length with increase in that length. This gives six possible measure-
ments of length. Construction of the various lines, however, showed
that the line through the point marking W, did not in all cases
intersect the posterior margin of the skull and that some of its values
were not commensurate with those of the other five measurements.
This line was therefore discarded as a measure. The measurements
used for length are thus as follows:
L,=Length at level of center of orbit.
L.=Length at level of termination of W:.
L;=Length at level of termination of W2.
I,4=Length at level of termination of Ws.
L;=Length at level of termination of W:.
The combined use of width and length measurements determined
by these methods made it possible to study related changes in lateral
and longitudinal growth. The changes can be nicely evaluated
along two axes to give a quantitative picture of skull changes.
Measurements for values in the sample are given in Tables 27 and 28.
GROWTH OF SKULL
Analysis of Growth
Using values of skull widths, skull lengths, and appropriate
values from the midline and orbital regions, we may obtain mean
values of the skull dimensions at desired size levels based on skull
OLSON: DIPLOCAULUS 137
length. By plotting these values a series of reconstructions of mean
skull patterns may be obtained. The series of stages shown in figure
18 (20, 40, 60, 80, 100, 120, and 140 mm. stages) has been developed
in this way. Lines between plotted points have, of course, been
sketched on the basis of knowledge of the marginal patterns of the
species. These drawings, while merely graphical expressions of
values calculated from the various equations, are most instructive
in a study of the general patterns of growth in D. magnicornis.
In order that plotting might be undertaken it was necessary to
determine equations for the regressions of each series of measurements
involved in skull length. It will be noted that some of the equations
are of the form Y=bX-+a and others of the form Y=bX*. These
indicate isogonic and heterogonic patterns of change, respectively.
The best fit for each regression was determined by comparison of
the squares of the coefficients of correlation, r? for the rectilinear
equation and p? for the logarithmic equation. In cases where p?
was appreciably greater than r?, the form Y=bX* was used, but
where r? was greater than p? or the two were approximately equal,
the form Y=bX-+a was used. The equations, in which X is skull
length and Y the measurement in question, are as follows:
PNP ace aca th nT hk ee Y=0.1076X —1.06
| cid Wenn PR eres Perr or regenerate teen Y= 0.829X+1.00
d £11 ARR oS LW te ork CM Ae ceee e moe Y= 0.248X +0.42
1&1} ROR Rie Sone ae a ah ae tty deh Oe nO Y = 0.117.X1.155
(ON) Cia me ee Anes REL LS Ea in aia ea Ohad ete Y= 0.1183.X1.172
U ARR ae eae sen, elias) Ser EN ae A MLO Nin Y=0.171X—2.49
Ope ee ret ee RON Wee een ene naga Y= 0.1442X +0.976
Wa eihex eee en ee eee eae Y= 0.82X —6.06
Wig Oke i RO au GN oh las La a eae aie Y=1.85X—15.53
Wai SP Be ce est Malte neh cee ok ions Y = 0.5443.X1.227
Wg Be ee rds ee et Pte Y = 0.2697.X1.417
PU giscce ee GS eh Re Re ence iad My casted lo ees Y = 0.2534.X1.418
W; (100 to 140 mm.).. cee eee ee Y= 0.0843.X1.9238
TEA CREE S SENG ALE DNL i 9 Sele ae eS alg le Y=1.04X—0.24
aera epone pect iee Me eicice: Me ES ioe Y=1.14X—6.2
Mgr A OR RY ae Sete Nit lal ocr See Y = 0.7875.X1.103
Lage EL So UR ee a NDE 1 Soe Y = 0.5769.X1.189
YRS BE SCRE ia eer Si SEM Ee APRS Y = 0.5663.X1.225
Each of the seventeen equations for the regression lines has been
determined by the method of least squares. From them the value
of Yc (calculated value of Y at the desired level of skull length)
has been determined, using the appropriate relationship. The
results of these determinations at 20 mm. intervals, beginning with
X=20, are given in Table 29. The plotted mean skull shapes are
1 For explanation of abbreviations see Table 2.
138 FIELDIANA: GEOLOGY, VOLUME 11
based on these figures. It should be noted that in the case of W;
it was necessary to use two equations to take into account the rapid
change in rate of relative growth that took place between the 80
and 100 mm. stages.
c 3
Fic. 18a. Mean growth stages of Diplocaulus reconstructed from estimating
equations. Xl. A, 20 mm. stage; B, 40 mm. stage; C, 60 mm. stage; D, 80 mm.
stage.
TABLE 29.—VALUES FOR PLOTTING MEAN SKULL STAGES OF DIPLOCAULUS
Skull
width (X) 20 40 60 80 100 120 140
Pm; 1.09 8.24 5.40 7.56 9.70 10.85 18.00
@S Fr 8.84 16.68 24.52 82.36 40.20 48.04 55.88
* Pa: 5.44 10.40 15.36 20.32 25.28 30.24 35.20
oe be B.7e: | 0s 1 Oe IS Ae ease ogg a5 00
m. «OS 8.96 8.92 14:35 20.10 25.80 82.30 38.80
CP Tou 0.00) 295. I lio 1a es S07 11249
505” 8.86 Ge 008s 19 Ses he sas) 21.16
2 Wi 10.34 26.74 43.14 59.54 (75.94 92.84 108.74
S W, 11.65 38.65 65.65 92.65 119.65 146.65 173.65
< Ws 21.50 50.40 82.70 117.80 154.80 198.60 233.90
3 W. 18.81 50.22 89.21 134.10 184.00 238.20 296.40
= 1
3 Ws 17.47 46.51 82.49 323-79" 940.60 341.60 459.60
§ Li 20.80 41.86 62.16 89.96 103.76 124.56 145.36
ect Aig, 2918) 44-08 67.78) 90888) © 118.98 18618. 168.98
S$ Ls; 21.40 46.10 72.00 98.90 126.60 154.70 188.40
SL, 20:30 46.30 75.50 105.60 187.80 171.10 205.50
1Two values given. The lesser (used in plotting) calculated from
Y=0.2584X1.413 and the greater from Y=0.0343.X1.923,
Fic. 18b. Mean growth stages of Diplocaulus reconstructed from estimating
equations. X14. E, 100 mm. stage; F, 120 mm. stage; G, 140 mm. stage.
139
—
140 FIELDIANA: GEOLOGY, VOLUME 11
Discussion of Changes in Skull Shape
It is apparent from the equations and from the plotted skull
outlines that vast changes took place in skull shape with change in
skull length in D. magnicornis. In dorsal aspect the skull at 20 mm.
has a shape not unlike that of skulls of certain other genera of Late
Paleozoic amphibians, notably Trimerorhachis. It is this fact that
et L2 Z4\L5
: SN
Fic. 19. ‘Stable’ and “unstable” parts of growing skulls in Diplocaulus
based on 80 mm. stage.
has resulted in the assignment of some of the smallest skulls of
Diplocaulus to the Trimerorhachidae. At this stage the horns are
poorly developed. The changes in the anterior part of the skull
are for the most part isogonic, except for the relationship of the
orbito-snout length to skull length. The shape changes proceed
without acceleration of growth rates. Similarly, length relationships
at levels L; and Le are best explained as isogonic. In essence this
means that changes in the zones limited by a line somewhere between
We and W3, with respect to width, and Le and Ls, with respect to
length, maintain a stable growth pattern in which the trends and
rates established very early do not modify materially throughout
the growth series (fig. 19). The lateral migration of Le, controlled
by the position of the posterior midline point of the frontal (involving
_Pmzj and Fr}, both isogonic) is also essentially isogonic. The zones
limited as noted above may be thought of as relatively stable parts
of the skull, parts in which the changes are simple and steady. It
is perhaps significant that the dermal surface of these zones overlies
the brain, includes the openings of the sensory organs, pineal, orbits
and external nares, and encompasses essentially the full extent of
_ the upper and lower jaws.
The remainder of the skull is subject to positive heterogonic
growth. The horns gradually appear between the 20 and 80 mm.
OLSON: DIPLOCAULUS 141
stages with their dominant direction of growth posterior, to produce
a pattern shown in figure 18, D. The posterior curvature developed
approaches that witnessed in adults of D. brevirostris, and were the
rate of W; maintained and the rate of L; accelerated a pattern closely
resembling that of these adults would result. The pattern in the
orbito-snout region, however, would be very different, and no
conceivable change from the 60 mm. stage or even the 40 mm.
stage of D. magnicornis could produce the pattern of D. brevirostris.
Between 80 and 100 mm. there tends to be a rapid alteration of
the direction of the axis of growth of the latero-posterior corners of
the skull. This is seen in a comparison of the second equation for
W; with that for Ls. The result is that lateral growth, which in-
creases rapidly, takes ascendancy over posterior growth, and the
horns become directed postero-laterally rather than posteriorly.
There is, in effect, a rotation of the horns. It occurs, of course,
through differential additions and resorptions of bone. The main
bone affected is the supratemporal, which expands rapidly postero-
laterally. The changes result in a pattern at 100 mm. decidedly
different from that at 80 mm.
It is not to be thought that this change occurred at precisely the
same skull length in all individuals. There is no known instance
in which any skull under 90 mm. shows marked effect of the accelera-
tion of lateral growth, and some skulls, almost to the 100 mm.
stage, show little evidence of rapid change. The usual stage of initia-
tion thus appears to be after the 90 mm. stage has been passed.
Two skulls at 101 mm. show pronounced effects, much like those
shown in the mean 100 mm. skull outline (see pls. 3 and 4). Almost
all skulls over 100 mm. have assumed a pattern in which lateral
extension of the horns is pronounced. There is, however, one strik-
ing exception, A.M. 4514, which, at 110 mm., maintains a pattern
not unlike that of the 80 mm. stage (compare fig. 18, D, and pl. 4, C).
If the regression line of W; for 20 to 80 mm. be extrapolated, it is
found that the value of W; of A.M. 4514 departs from it but little,
whereas this value deviates markedly from the line plotted from
the equation for W; from 100 to 140 mm. This skull appears to
represent a case of extreme retardation of the onset of rapid lateral
growth, retardation, of course, only in the relationship to skull
size as measured along the midline and not necessarily in time.
From the evidence available it seems that acceleration in relative
lateral growth of the latero-posterior region of the skull may begin
slightly before the 90 mm. stage and usually develops between 90 mm.
142 FIELDIANA: GEOLOGY, VOLUME 11
and 100 mm.; but it may in some instances be delayed until at least
the 110 mm. stage is reached. Moderate attainment of what may
be considered the adult pattern is commonly attained at about 100
mm.
The tendency toward increasingly rapid lateral growth in the
latero-posterior zone is maintained until at least the 130 mm. stage.
That it could have continued much beyond this stage seems improb-
able, since an unwieldy structure, foreshadowed in the reconstruction
of the 140 mm. stage, would develop. There is only slight evidence
of the course of events beyond the 180 mm. stage. One skull, U.C.
637, measures 185 mm. in length, but distortion and breakage make
the measurement somewhat unreliable. As reconstructed, the long
horns are directed posteriorly (pl. 6) but it is evident that the
horns have been rotated medially a minimum of some 30 degrees.
The pattern with the horns in more normal position would approxi-
mate that of the 140 mm. reconstruction moderately closely. A.M.
4484 measures 147 mm. in length. The specimen is badly crushed
and this may have increased the length several millimeters. The
horns are weathered and in part missing; they extend only a short
distance beyond the otic notch. It may be that full knowledge of
the horns would show a pattern not unlike that of the 140 mm.
reconstruction. This, however, must be conjectural, for it is possible,
on the basis of what is known of the skull, that the horn development
was more nearly like that shown in the 120 mm. reconstruction. In
any event, it is quite certain that the horns of A.M. 4484 did not
assume the pattern indicated by extrapolation to a 145 mm. stage.
There is vague evidence, then, of retardation of horn growth in very
large skulls, but this is based on a single, badly preserved specimen
and is at best only suggestive.
The zones in which the rapid changes take place may be thought
of as decidedly plastic in contrast to the stable areas noted previously.
The causes and effects of the changes in the plastic zones must remain
somewhat obscure, but we may speculate on them briefly to good
advantage. If the ancient amphibians followed the general patterns
of development witnessed among anurans and urodeles, we should
expect some evidence of a marked break in growth continuity at
some stage in their development. The stage of metamorphism
varies widely among modern groups; bufonids, for example, pass
through metamorphism when relatively small, and ranids when
relatively large. The relative amount of growth after metamorphism
is thus very different in the two groups. There is no evidence of a
break in rates of change in the plastic portions of the skulls of
OLSON: DIPLOCAULUS 143
D. magnicornis from the 14 mm. to about the 90 mm. stage. What
occurred prior to the 14 mm. stage we do not know. There is,
however, an abrupt change at about 90 mm. and it seems logical
to suppose that this change indicates the initiation of the adult
condition. It has been noted earlier (pp. 102-104) that there are
some puzzling circumstances surrounding the condition of the
_ vertebrae. Very large, fully matured vertebrae are developed in a
few large specimens, U.C. 564 for example, among the specimens
that compose the sample of D. magnicornis. Other specimens, with
approximately the same skull lengths, however, have much smaller
vertebrae. It may be that the large vertebrae, found in very few
instances, represent a pattern that developed with complete maturity,
and that the smaller vertebrae, which in various characteristics are
like those of specimens with skulls under 90 mm. in length, represent
vertebrae that have not undergone this change. If so, it would
seem that in many instances maturation of the postcranial axial
skeleton was retarded and perhaps never fully accomplished. We
have noted at least one instance of retardation of change of rate in
lateral growth of the skull and there is less clear evidence of other
cases. What evidence there is suggests that neoteny may have
played an important part in the development of Dviplocaulus,
particularly in the postcranium. The environment, entirely aquatic
so far as can be determined, is one in which this phenomenon is
commonly encountered.
It is evident that the rapid change in the skulls must have been
correlated with important functional changes. Until such time as
adequate evidence on the function of the lateral projections of the
skull may come to light, it is impossible to make a critical analysis
of the nature of the functional changes. It is clear that the areas
housing the brain and sense organs and the regions of the jaws
and dentition were not drastically modified. Changes must be related
primarily to mobility of the animals. It would appear that smaller
individuals had a capacity for more active swimming than the fully
matured animals. If there was a membrane attached to the horns
and used for locomotion, or any other purpose, it could hardly have
been functionally important below the 90 mm. stage. It might
have developed beyond this stage to an effective level for locomotion
and have offset to some degree the effects that the change in skull-
shape presumably had in retarding activity. This would suggest
a rather marked change in the method of locomotion and, pre-
sumably, in the postcranial structures associated with locomotion.
Although there is some evidence of decided change in the vertebrae
144 FIELDIANA: GEOLOGY, VOLUME 11
from one specimen, it is evident that most specimens did not undergo
full development in this region. The development of such a mem-
brane, which is purely hypothetical, or of a decided flattening of
the body, which the ribs of some specimens suggest, could have been
of but moderate use in locomotion. It might, however, have func-
tioned in a very different way. As mobility decreased, protection
from predators must have become a more difficult problem. Con-
cealment rather than escape must have been important. In a number
of flat animals—skates or flounders, for example—concealment is
attained by covering the body with bottom sediment. It is possible
that Diplocaulus adopted this method of concealment, using a mobile
lateral portion of the flattened body as a mechanism for covering.
The environment suggested by the sediments in which many speci-
mens of D. magnicornis occur, sluggish or quiet waters, fits this
interpretation. Indications of dry periods also suggest that burial
would be of advantage to the animals. On the other hand, speci-
mens of D. brevirostris, with a probable stream habitat, did not
develop such large latero-posterior horns, the sedentary habits, or,
presumably, the decidedly flattened bodies.
THE PROBLEM OF VARIABILITY
One of the most striking features of a series of skulls of D. magni-
cornis is the wide diversity of shapes. Even series containing only
relatively large skulls, those over 100 mm. in length, show this
phenomenon. The conclusion that the species is highly variable
(see Douthitt, 1917, for example) has followed. The best statement
of variability, in the biological sense, is made through use of the
coefficient of variability of Pearson, determined from the formula
V=100c/M, in which M is the mean of the sample. It seems
quite certain that statements to the effect that Diplocaulus is highly
variable are based upon the concept of dispersal about a mean ex-
pressed by this coefficient. If this is not the case, they have no
apparent meaning. The studies that have been made upon Diplo-
caulus in the preparation of the present paper and a consideration
of the real meaning of V lead to serious doubts concerning the
appropriateness of the application of V to a case such as that pre-
sented by this animal.
Relative variability can have meaning only in terms of some
empirically determined or arbitrarily assigned standard. Simpson
and Roe (1939) have pointed out that, for recent samples among
the vertebrates, values of V between 4 and 7 represent coefficients
Cee a
OLSON: DIPLOCAULUS 145
of variability most commonly encountered and this gives a reason-
able basis for evaluation of samples to which the concept may be
applied legitimately. If, therefore, values much higher than 7 are
obtained we may be justified in believing that the sample analyzed
is highly variable, and, assuming the sample to be homogeneous,
that this is true biological variability. It is an easy step from this
basis to the determination of the value of V for the various characters
of D. magnicornis and comparisons with similar measurements from
other species. In fact, it is quite simple to “‘prove”’ by this means
that in a number of characteristics D. magnicornis is highly variable.
Numerous characters have been analyzed in this way in the course
of the study and values ranging from 15 to 30 have been obtained.
The procedure has been outlined and carried out in this study only
because it appears to be a quantitative application of the thought
processes that have been followed to arrive at the conclusion that
the species is highly variable. The conclusion reached is meaning-
less, for it involves a misapplication of the concept of V.
The coefficient of variability has been applied most commonly,
among vertebrates, to teeth and skeletal elements in fossil mammals.
Teeth, provided with an enamel covering, once fully formed, change
only through wear. Mammalian bones, in most instances, cease to
increase in size as the animal attains maturity. In these instances,
determination of the dispersal of values about the sample mean
expresses real biological variability and the coefficient of variability
may properly be used. The bones of amphibians and reptiles, at
least in the majority of cases, do not have a determinable terminal
growth. Although the growth is clearly slower in late stages, it
does not cease during the lifetime of an individual. Any determina-
tion of variability in terms of V must necessarily reflect the effects
of changes in size and proportion continuing so long as growth con-
tinues, and is thus not commensurate with values determined from
a sample, such as one of mammals, in which growth has ceased.
Values obtained from a sample composed of individuals that have
not reached a stage of cessation of growth do not express variability
in its true biological sense. This applies not only to amphibians and
reptiles but also to such features of mammals as the antlers of deer
and, probably, skull shape in cases where cranial areas are underlaid
by sinus systems (for example, in sloths, titanotheres, etc.) or where
excrescences, such as the “‘horns” of titanotheres, continue to grow
after maturity has been attained. It is recognized that continuing
change of the antlers in deer gives no basis for calling the species
highly variable, nor does it give a basis for calling the antlers highly
146 FIELDIANA: GEOLOGY, VOLUME 11
variable. This has been, perhaps, less clearly recognized in other
groups of mammals, for certainly such forms as sloths and titan-
otheres, in which cranial sinuses are highly developed, have seemed
to present a rather bewildering array of variability. The effects
upon taxonomy of such misinterpretation may be disastrous.
The case of D. magnicornis appears to be one common to the
amphibians and to many reptiles, but one in which certain growth
characteristics impart particular emphasis to the factors involved.
It cannot be denied, I believe, that there exists in D. magnicornis
a theoretical or, better, a potential variability, but in view of the
conditions of growth the problem of determination of this variability
can have no satisfactory answer. Only were the animals to reach
a stage at which growth definitely ceased would variability commen-
surate with that expressed by V exist. Tests of variability at any
stage, either before or after cessation of growth, essentially measure
the differing effects of relative growth between individuals, but
only when growth has ceased is there a common basis among speci-
mens for determination of biological variability. Until that stage
is reached, and probably in D. magnicornis it never was, variability
as expressed by V is potential only.
There are several approaches to the problem, but each contains
a fallacy or poses an insurmountable sampling problem. The sound-
est approach, in theory, is to deal with a sample in which growth
has slowed nearly to the point of cessation. Such a sample, rarely
obtained and difficult to recognize among living lower vertebrates,
is a virtual impossibility among fossils. An approach through
measurement of variability at different growth stages measured by
some dimension or by time may appear attractive. It is not un-
common practice in dealing with mammals, particularly with man,
to measure variation of an age group in one character or another,
but here, as in reptiles or amphibians, what is measured is not
biological variability but factors pertaining to differential growth
in time. Determinations for age groups of amphibians or reptiles
can properly be compared to such data, provided that appropriate
time relationships can be established, but this is not a comparison
of variability as implied in the coefficient of variability.
It seems clear that the concept of V cannot be applied to any
group during growth in the same way that it can be applied after
the termination of growth. Various techniques may be used for
study of the dispersal of values about regression lines and these
may be applied to growth series. While they are valuable for com-
OLSON: DIPLOCAULUS 147
parative purposes, from none does a concept of variability com-
parable to that of V emerge, and we remain without a basis for
comparison of variability in the sense desired. This follows simply
from the fact that none can be based upon the physiological processes
basic to the concept of variability, in the absence of those processes
in the groups considered.
If we cannot then determine the scope of variability in D. magni-
cornis, what value can be derived from analyses of the patterns of
growth? First, as discussed in the preceding section, the general
nature of changes in skull pattern may be determined. Second,
the extent of deviation from the mean pattern at appropriate levels
may be determined. This may be taken directly from the regression
diagrams or may be calculated. As has been pointed out above,
this is not a measure of variability of the skulls nor does it provide
a basis for determination of variability. It does, however, give a
basis for analysis of the great differences in skulls of approximately
the same size in terms of skull length.
There appear to be two principal factors entering into the develop-
ment of the wide differences in skull shapes: (1) differential growth
rates of various parts of the skull; (2) differences in the stages of
onset of acceleration of growth in latero-posterior parts of the skulls.
Differential growth rates may be determined readily from the
equations that are given on page 187 for any stage of skull develop-
ment in terms of skull length. We may compare, for example, the
rate of growth along the midline and that of the horn tip (W;) as
expressed above the 100 mm. level, by the equation Y=0.0343.X1-928,
We find that as the length of skull increases from 100 to 110 mm.,
skull width increases from 240 to 282 mm. Thus over this interval
width is increasing at a mean rate of about 4:1 over length, with,
of course, increased relative rate from 100 to 110 mm. The increase
between the 110 and 120 mm. stages of skull length is 59 mm., from
282 to 341 mm., or a mean ratio of about 6:1. The case selected
for illustration of method is the most extreme in the skull but the
same principle applies to all cases of relative heterogonic growth.
A 10 mm. change in skull length is relatively minor in large skulls
and the difference occasioned by it is not particularly apparent
under casual observation. Thus two skulls that appear to be
about the same length may show striking differences when compared
with respect to width. It is rather common practice to think of
size in terms of an axial measurement, skull length in this instance,
and hence it may appear that two skulls of the same “‘size’”’ are very
148 FIELDIANA: GEOLOGY, VOLUME 11
different. Furthermore, the tendency to think of variability in
terms of size is normal since the importance of deviations from the
mean in linear dimensions is directly related to the magnitude of
the mean. Thus may follow the conclusion—erroneous, as pointed
out above—that the length-width relationships are indicative of
high variability.
The second important factor is the stage of growth acceleration
in the latero-posterior parts of the skull. This applies most strik-
ingly in the case of Ws, in which there is an abrupt change of con-
siderable magnitude. It applies less, but in an equally real manner,
in all cases of heterogony in which there is steady acceleration.
This is a somewhat more subtle relationship and, on the basis of
data available for Diplocaulus, not subject to critical analysis. It
is evident, however, as noted in the preceding paragraphs, that
skulls of nearly the same length have widely different values of
W:, which again will be used as an example. It is also evident that
there is a change of rate of growth of considerable magnitude for
W; between the 80 and 100 mm. stages in skull length. There is,
however, evidence that some skulls have participated less and some
more in this change at particular levels than have others. Such a skull
is that of A.M. 4514, an extreme case, showing a value of 198 mm.
for Ws; at skull length of 110 mm., a deviation of —89 mm. from the
mean, Yc=282. Clearly it has followed a growth pattern different
from that of other skulls of approximately the same length. So
far as this one specimen is concerned there has been no appreciable
change from the rates predicted for skull growth below 80 mm. of
skull length. Other skulls show the effect of differences in change
of rates either in excess of that determined, with positive deviations,
or less than the determined mean change, with negative deviations.
This effect produces a wide dispersal of points around the regres-
sion line. But the dispersal is not a function of variability in the
biological sense. We may conceive a stage in the growth of Diplo-
caulus, purely hypothetical so far as the evidence from the sample
is concerned, at which growth has virtually ceased and from which
an approximation of real variability could be determined. The
dispersal about the regression line, that is, the mean value, Yc,
properly determined for any particular regression at a particular
value of X, does not necessarily bear any direct relationship to the
variability at that hypothetical stage. It is exceedingly important
to recall in this instance that skull length does not necessarily repre-
sent even a relative time scale, although it may approximate it,
OLSON: DIPLOCAULUS 149
and that time does not necessarily bear a close relationship to the
hypothetical stage of growth cessation.
The effects discussed above offer probable “explanations” of
why the skulls of D. magnicornis give the appearance of high varia-
bility. In terms of them it is clear that the specimens of a single
species may exhibit wide diversity of form without respect to actual
variability. We have no evidence, nor does it appear probable that
evidence can ever be obtained, of the nature of biological variability
in this species. It was stated above that many genera of Permian
amphibians and reptiles seem to exhibit a wide diversity of form and
that this phenomenon was one of the problems to be attacked in
this paper. It seems probable that the “explanations’’ offered in
these closing pages may apply to at least some of the other cases.
Differential growth rates of different parts of the skeleton probably
have played a very important part in producing wide diversity in
structures in specimens that are quite similar in one or more dimen-
sions. Different stages of appearance of adult characteristics become
important principally when some important change of growth rates
occurs at this threshold, but apply in lesser degree in all cases of
heterogonic growth. They may become of particular importance in
instances in which various foramina and fossae are characteristic of
one growth stage but not of another, as in changes of infantile to
adult circulatory patterns, and in instances in which bone dimensions
are in part a function of the degree of ossification.
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PLATES
Qasoon>
A.M. 4528A, Ski=14 mm.
U.C. 206, Ski=23 mm.
U.C. 1660, Ski=19 mm.
A.M. 4523B, Ski=24 mm.
A.M. 4752, Ski=31 mm.
U.C. 224, Ski=46 mm.
A.M. 4485, Ski=50 mm.
PLATE 1
Diplocaulus magnicornis Cope
SOR SS
A.M. 4589, Ski=63 mm.
U.C. 222, Ski=65 mm.
U.C. 1668, Ski=65 mm.
U.C. 1658, Ski=68 mm.
U.C. 228, Ski=70 mm.
. A.M. 4597, Ski=73 mm.
Plate 1
Fieldiana: Geology, Volume 11
Sane
U.C. 1656, Ski=75 mm.
U.C. 1657, Ski=75 mm.
U.C. 1652, Ski=80 mm.
A.M. 4511, Ski=81! mm.
1 Approximate.
PLATE 2
Diplocaulus magnicornis Cope
A.M. 4491, Ski=82 mm.
U.C. 410, Ski=85 mm.
U.C. 1650, Ski=89 mm.
P12689, Ski=89 mm.
Fieldiana: Geology, Volume 11 Plate 2
‘ «
det
Lint
“4
Sane
A.M. 4478, Ski=105! mm.
A.M. 4494, Ski=105! mm.
A.M. 4514, Ski=110 mm.
U.C. 564, Ski=114 mm.
1 Approximate.
PLATE 4 ©
Diplocaulus magnicornis Cope
Taxes
A.M. 4498, Ski=114 mm.
A.M. 4466, Ski=115 mm.
A.M. 4467, Ski=118 mm.
U.C. 1654, Ski=116! mm.
Fieldiana: Geology, Volume 11 Plate 4
PLATE 5
Diplocaulus magnicornis Cope
A. U.C. 636, Ski=119 mm. C. A.M. 4501, Ski=130' mm.
B. A.M. 4472, Ski=127 mm.
1 Approximate.
Fieldiana: Geology, Volume 11 Plate 5
PLATE 6
Diplocaulus magnicornis Cope
A. U.C. 1817, Ski=129 mm. C. A.M. 4484, Ski=147 mm.
B. U.C. 637, Ski=135 mm.
Fieldiana: Geology, Volume 11 Plate 6
PLATE 7
Diplocaulus brevirostris sp. nov.
A. U.C. 1661, Ski=107 mm. C. U.C. 1655, Ski=120! mm.
B. A.M. 4470, Ski=119 mm. D. U.C. 1648, Ski=136 mm.
Holotype of species.
1 Approximate.
Fieldiana: Geology, Volume 11 Plate 7
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